Wikipedia:WikiProject Mathematics/PlanetMath Exchange/15-XX Linear and multilinear algebra; matrix theory

Where am I?

15-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

 * PM: anti-diagonal matrix, id=6964 -- WP: anti-diagonal matrix -- Status: C
 * Copied and made suitable for WP. Jitse Niesen (talk) 13:58, 24 July 2005 (UTC)


 * PM: antipodal, id=4731 -- WP: antipodal point -- Status: M
 * The PM article has some topological information on the antipodal map, which is now merged into the WP article. Jitse Niesen 21:38, 19 Mar 2005 (UTC)


 * PM: Cholesky decomposition, id=1287 -- WP: Cholesky decomposition -- Status: M
 * The WP article had most of the information of the PM article and quite a bit more. I merged the remaining bits of the PM article into the WP article and rewrote it in the process. Jitse Niesen 21:38, 19 Mar 2005 (UTC)


 * PM: conjugate transpose, id=4382 -- WP: conjugate transpose -- Status: M
 * The WP article lacked some alternative names and symbols and some basic properties, which are now included. Note that the related article Hermitian adjoint could use some clean-up. Jitse Niesen 15:49, 22 Mar 2005 (UTC)


 * PM: corollary of Schur decomposition, id=4413 -- WP: Schur decomposition -- Status: N
 * The corollary is that any normal matrix is unitarily similar to a diagonal matrix. This is mentioned in Schur decomposition and spectral theorem. The PM article includes a proof which we don't need. Jitse Niesen 15:49, 22 Mar 2005 (UTC)


 * PM: covector, id=3719 -- WP: dual space -- Status: A
 * PM article is two lines and only mentioned the definition. I created a redirect to dual space, where the name covector is mentioned. Jitse Niesen 15:49, 22 Mar 2005 (UTC)


 * PM: derivative of homogeneous function, id=6390 -- WP: homogeneous function -- Status: M
 * PM article states that if f is homogeneous of degree r, then the derivative of f is homogeneous of degree r &minus; 1 (it also includes a proof which we do not need). This should be mentioned in an article on homogeneous functions, which unfortunately does not exist (either that or I could not find it). See also homogeneous (mathematics). Jitse Niesen 17:37, 24 Mar 2005 (UTC)


 * PM: diagonal matrix, id=4411 -- WP: diagonal matrix -- Status: M
 * Two sentences were merged into the WP article, which was largely complete. Jitse Niesen 17:37, 24 Mar 2005 (UTC)


 * PM: diagonalization, id=1960 -- WP: diagonalizable matrix -- Status: A


 * PM: diagonally dominant matrix, id=4512 -- WP: Diagonally dominant matrix -- Status: N
 * PM article only defines what diagonally dominant is. I think that is not enough to warrant an article. Jitse Niesen 23:20, 24 Mar 2005 (UTC)
 * I created the article today. Diagonal dominance has a number of important uses in numerical linear algebra (tho' I only started a list).  Could someone add the stub tag?  And is there a category for numerical linear algebra?  (Or just linear algebra and numerical analysis separately?)  Thanks.Lunch 18:50, 23 May 2006 (UTC)


 * PM: eigenvalue (of a matrix), id=4397 -- WP: eigenvalue -- Status: M
 * Phew ... this was a lot of work since the WP article was in a rather bad state, although it was largely complete. Now, the WP article is completely rewritten and some statements from the PM article are merged in. Jitse Niesen 22:17, 19 Apr 2005 (UTC)


 * PM: eigenvalue problem, id=1474 -- WP: various (see below) -- Status:
 * This is a tough one. The PM article is a wide-ranging discussion. Synopsis of PM article (with corresponding WP articles): definition (eigenvalue, eigenvector), differential eigenvalue problems (differential operator, spectrum of an operator, Sturm-Liouville problem), matrix eigenvalue problems (again eigenvalue), numerical eigenvalue problems (eigenvalue algorithm, QR algorithm). I don't know what to do with this; I think we should merge in some material in the mentioned WP-articles and leave it with that; I already expanded the WP article on the QR algorithm. Jitse Niesen 22:17, 19 Apr 2005 (UTC)
 * Update: The new article eigenvalue, eigenvector and eigenspace has similar scope as the PM article.


 * PM: eigenvalues of orthogonal matrices, id=4240 -- WP: eigenvalue, orthogonal matrix -- Status: N
 * PM article is a longwinded (IMHO) proof that all eigenvalues of orthogonal matrices have unit modulus; a fact which can be more easily proved from the isometry property. I added a statement to that effect. Jitse Niesen 22:17, 19 Apr 2005 (UTC)


 * PM: eigenvector, id=1497 -- WP: eigenvector -- Status: A


 * PM: equitable matrices of order 2, id=6675 -- No WP article -- Status: N
 * PM article contains a trivial proof of the form of 2 &times; 2 equitable matrices. Jitse Niesen 21:19, 25 Mar 2005 (UTC)


 * PM: equitable matrix, id=6674 -- No WP article -- Status: N
 * A matrix is equitable if it satisfies $$a_{ij}=a_{ik} a_{kj}$$. I doubt this concept is notable enough to be included in WP. Indeed, a Google search turned up only two references to the term "equitable matrix" and I could find only one article in MathSciNet (Parker, Matrices in the market place, Math. Mag. 38:125--128, 1965), describing an application in economics also listed on PM. On the other hand, PM also has a reference to "Elementary matrix theory" by H. Eves. Jitse Niesen 12:37, 4 Apr 2005 (UTC)


 * PM: exactly determined, id=1253 -- WP article: system of linear equations -- Status: M
 * Entire content of PM article: "An exactly determined system of linear equations has precisely as many unknowns as equations and is hence soluble." Jitse Niesen 21:19, 25 Mar 2005 (UTC)
 * I now mentioned the concept exactly determined at system of linear equations. -- Jitse Niesen (talk) 23:18, 1 September 2005 (UTC)


 * PM: example of non-diagonalizable matrices, id=5686 -- WP: diagonalizable matrix -- Status: M


 * PM: free vector space over a set, id=4196 -- WP: free module -- Status: M
 * PM article explains the construction of a free vector space. As far as I can tell, this construction also works for modules, so I merged it into the WP article on free modules. Jitse Niesen 17:29, 21 Apr 2005 (UTC)


 * PM: Hadamard conjecture, id=5524 -- WP: Hadamard matrix -- Status: A


 * PM: Hadamard matrix, id=3605 -- WP: Hadamard matrix -- Status: A
 * In fact, the PM and WP articles are very similar. I only added a URL listed in the PM article as a reference to the WP article and did some copy-editing. Jitse Niesen 17:29, 21 Apr 2005 (UTC)


 * PM: Hessenberg matrix, id=1475 -- WP: Hessenberg matrix -- Status: A


 * PM: homogeneous function, id=6381 -- WP: homogeneous function -- Status: A
 * I created the WP article homogeneous function by copying the relevant parts of the disambiguation page homogeneous. Jitse Niesen 00:01, 22 Apr 2005 (UTC)


 * PM: If A \in M_n(k) and A is supertriangular then A^n=0, id=4438 -- WP: triangular matrix -- Status: N
 * PM article is a rather indirect proof of the nilpotency of strictly triangular matrices. Jitse Niesen 23:48, 22 Apr 2005 (UTC)


 * PM: invariant subspace, id=1962 -- WP: invariant subspace -- Status: A


 * PM: Jacobi determinant, id=1268 -- WP: Jacobian, substitution rule -- Status: A
 * It would be nice to have an example in substitution rule for the case of multivariate integrals, but I don't like to PM example very much. Jitse Niesen 23:48, 22 Apr 2005 (UTC)


 * PM: Jacobi's Theorem, id=4156 -- WP: skew-symmetric matrix -- Status: M
 * The theorem was mentioned on WP, but not the fact that it is called "Jacobi's theorem". Jitse Niesen 23:48, 22 Apr 2005 (UTC)


 * PM: Kronecker product, id=4163 -- WP: Kronecker product -- Status: M
 * I spun off parts of tensor product and matrix multiplication and added material from the PM article and some more. Jitse Niesen 22:00, 8 Jun 2005 (UTC)


 * PM: least squares, id=1195 -- WP: least squares -- Status: M
 * Unfortunately, the PM article, which is copied from another source, is rather bad. Jitse Niesen 22:00, 8 Jun 2005 (UTC)
 * I actually did this some time ago, making a terrible mistake, fortunately caught by Michael Hardy. Jitse Niesen (talk) 23:01, 19 July 2005 (UTC)


 * PM: linear algebra, id=2530 -- WP: linear algebra -- Status: A
 * WP article has a good elementary intro but degenerates after that (e.g., it lists a dozen equivalent statements for "A is invertible"), but the PM article does not treat any advanced parts. In short, WP article needs a serious overhaul. Jitse Niesen (talk) 23:01, 19 July 2005 (UTC)


 * PM: linear least squares, id=1197 -- WP: linear least squares -- Status: A
 * Jitse Niesen (talk) 23:01, 19 July 2005 (UTC)


 * PM: linear manifold, id=5435 -- WP: affine transformation -- Status: A
 * A linear manifold is just another name for an affine space, which is treated briefly but adequately at affine transformation. I created a redirect from linear manifold. Jitse Niesen (talk) 23:01, 19 July 2005 (UTC)


 * PM: LU decomposition, id=1227 -- WP: LU decomposition -- Status: A
 * Jitse Niesen (talk) 13:58, 24 July 2005 (UTC)


 * PM: matrices of special form, id=5670 -- WP: list of matrices -- Status: M
 * Our list is at least twice as long, but still, PM had two entries which we did not have: Anti-diagonal matrix and Pascal matrix. Jitse Niesen (talk) 13:58, 24 July 2005 (UTC)


 * PM: matrix exponential, id=4162 -- WP: matrix exponential -- Status: A
 * But I could still add some more to the WP article. -- Jitse Niesen (talk) 22:25, 6 August 2005 (UTC)


 * PM: matrix operations, id=4734 -- WP: matrix (mathematics) -- Status: A
 * I added the redirect matrix operation &rarr; matrix (mathematics). -- Jitse Niesen (talk) 22:25, 6 August 2005 (UTC)


 * PM: nilpotent matrix, id=3520 -- WP: nilpotent matrix -- Status: A
 * Jitse Niesen (talk) 22:25, 6 August 2005 (UTC)


 * PM: nilpotent transformation, id=1961 -- WP: nilpotent matrix -- Status: M
 * Almost done merging, only the section on flags needs to be copied. -- Jitse Niesen (talk) 22:25, 6 August 2005 (UTC)
 * Now done. -- Jitse Niesen (talk) 22:33, 10 August 2005 (UTC)


 * PM: non-zero vector, id=5450 -- WP: zero vector -- Status: A
 * Entire content of PM article is "A non-zero vector in a vector space V is a vector that is not equal to the zero vector in V." which seems all there is to say and would end up at VfD here. -- Jitse Niesen (talk) 22:25, 6 August 2005 (UTC)
 * I later found out that zero vector is a redirect to null vector (vector space), so non-zero vector also redirects there now. -- Jitse Niesen (talk) 22:33, 10 August 2005 (UTC)


 * PM: normal equations, id=1144 -- WP: linear least squares -- Status: A


 * PM: off-diagonal entry, id=4459 -- Not on WP -- Status: N
 * Entire content of PM article is "Let $$A=(a_{ij})$$ be a square matrix. An element $$a_{ij}$$ is an off-diagonal entry if $$a_{ij}$$ is not on the diagonal, i.e., if i &ne; j." -- Jitse Niesen (talk) 22:33, 10 August 2005 (UTC)


 * PM: orthogonal matrices, id=1176 -- WP: orthogonal matrix -- Status: M
 * PM had the interesting fact that orthogonal matrices, especially Householder reflections and Givens rotations, are important in numerical analysis. For the rest, the WP article is far more complete. -- Jitse Niesen (talk) 23:18, 1 September 2005 (UTC)


 * PM: orthogonal vectors, id=1285 -- WP: orthogonality -- Status: A
 * Jitse Niesen (talk) 23:18, 1 September 2005 (UTC)


 * PM: overdetermined, id=1255 -- WP: system of linear equations -- Status: M
 * I just mentioned the word overdetermined in system of linear equations. -- Jitse Niesen (talk) 23:18, 1 September 2005 (UTC)


 * PM: partitioned matrix, id=4150 -- WP: block matrix -- Status: A
 * Jitse Niesen (talk) 00:56, 4 September 2005 (UTC)


 * PM: Peetre's inequality, id=4681 -- WP: Peetre's inequality -- Status: C
 * I copied the inequality, but left out the proof. -- Jitse Niesen (talk) 00:56, 4 September 2005 (UTC)


 * PM: pentadiagonal matrix, id=3927 -- WP: pentadiagonal matrix -- Status: C
 * Jitse Niesen (talk) 23:10, 6 September 2005 (UTC)


 * PM: principle components analysis, id=1493 -- WP: principal components analysis -- Status: A
 * WP article is longer and covers all the main points of the PM article. Jitse Niesen (talk) 23:12, 9 September 2005 (UTC)


 * PM: proof of Cayley-Hamilton theorem, id=2802 -- WP: Cayley-Hamilton theorem -- Status: A
 * WP already has a different proof. Jitse Niesen (talk) 23:12, 9 September 2005 (UTC)


 * PM: proof of Schur decomposition, id=5424 -- WP: Schur decomposition -- Status: M
 * This is a constructive proof which is used in numerical linear algebra. Jitse Niesen (talk) 17:56, 8 October 2005 (UTC)


 * PM: pseudoinverse, id=1281 -- WP: pseudoinverse -- Status: A
 * WP article is clearly more complete. Jitse Niesen (talk) 23:12, 9 September 2005 (UTC)


 * PM: Schur decomposition, id=4380 -- WP: Schur decomposition -- Status: A
 * While the Wikipedia article was similar to the PM article, it did need to be explanded a bit, inter alia with the proof mentioned two items above. Jitse Niesen (talk) 17:56, 8 October 2005 (UTC)


 * PM: singular value decomposition, id=1171 -- WP: singular value decomposition -- Status: M
 * The PM article notes that the SVD can be used to solve least-squares problems. I copied this statement. Jitse Niesen (talk) 17:56, 8 October 2005 (UTC)


 * PM: skew-symmetric matrix, id=977 -- WP: skew-symmetric matrix -- Status: M
 * I merged properties 3 and 4 from the PM article into our article. Jitse Niesen (talk) 17:56, 8 October 2005 (UTC)


 * PM: square matrix, id=1472 -- WP: matrix (mathematics) -- Status: A
 * WP article is more complete. Jitse Niesen (talk) 22:48, 5 October 2005 (UTC)


 * PM: strictly upper triangular matrix, id=4381 -- WP: triangular matrix -- Status: A
 * The PM article only contains the definition, which was already present in the WP article. Just to be sure, I redirected strictly upper triangular matrix and strictly upper triangular matrix to triangular matrix. -- Jitse Niesen (talk) 17:18, 10 October 2005 (UTC)


 * PM: symmetric matrix, id=974 -- WP: symmetric matrix -- Status: A
 * PM article only contains the definition, but WP article has more. -- Jitse Niesen (talk) 17:18, 10 October 2005 (UTC)


 * PM: theorem for normal triangular matrices, id=4412 -- WP: normal matrix, triangular matrix -- Status: M
 * The theorem is that every normal triangular matrix is diagonal. I added this to the WP articles, with the proof condensed to one line. -- Jitse Niesen (talk) 17:18, 10 October 2005 (UTC)


 * PM: triangular matrix, id=1483 -- WP: triangular matrix -- Status: M
 * PM article included the fact that the eigenvalues of a triangular matrix are the diagonal entries; I added this to the WP article which was in all other respects more complete. -- Jitse Niesen (talk) 17:18, 10 October 2005 (UTC)


 * PM: tridiagonal matrix, id=1480 -- WP: tridiagonal matrix -- Status: A
 * PM only contains the definition, and WP quite a bit more. -- Jitse Niesen (talk) 14:39, 5 November 2005 (UTC)


 * PM: under determined, id=1260 -- WP: system of linear equations -- Status: A
 * I made redirects from Under determined and Underdetermined to System of linear equations. -- Jitse Niesen (talk) 14:39, 5 November 2005 (UTC)


 * PM: unit triangular matrix, id=4375 -- WP: triangular matrix -- Status: A
 * I created a redirect from Unit triangular matrix to Triangular matrix, where this concept is mentioned. -- Jitse Niesen (talk) 14:39, 5 November 2005 (UTC)


 * PM: unitary, id=1042 -- WP: unitary space, unitary operator, unitary matrix -- Status: A
 * PM says that a unitary space is a complex vector space with a distinguished positive definite Hermitian form, which serves as inner product. I am not sure we need this definition here. The other concepts treated by PM are adequately covered in Unitary operator and Unitary matrix. -- Jitse Niesen (talk) 14:39, 5 November 2005 (UTC)


 * PM: vector subspace, id=624 -- WP: vector subspace -- Status: M
 * PM article mentioned the sum of two subspaces, and the orthogonal complement. I added both to WP. -- Jitse Niesen (talk) 19:42, 5 November 2005 (UTC)


 * PM: zero map, id=5416 -- WP: 0 (number) -- Status: A
 * Redirect created, analogous to zero function which also redirects to 0 (number). -- Jitse Niesen (talk) 19:42, 5 November 2005 (UTC)


 * PM: zero vector space, id=5414 -- WP: examples of vector spaces -- Status: A
 * Utter triviality, but I created the redirect nonetheless. -- Jitse Niesen (talk) 19:42, 5 November 2005 (UTC)


 * PM: An example for Schur decomposition, id=7299 -- WP guess: An example for Schur decomposition -- Status:


 * PM: derivation of 2D reflection matrix, id=7262 -- WP guess: derivation of 2D reflection matrix -- Status:


 * PM: derivation of rotation matrix using polar coordinates, id=7261 -- WP guess: derivation of rotation matrix using polar coordinates -- Status:


 * PM: equitable matrix for money exchange, id=6695 -- WP guess: equitable matrix for money exchange -- Status:


 * PM: Euler's theorem on homogeneous functions, id=7121 -- WP guess: Euler's theorem on homogeneous functions -- Status:


 * PM: example of rotation matrix, id=6902 -- WP guess: example of rotation matrix -- Status:


 * PM: Frobenius inequality, id=7360 -- WP guess: Frobenius inequality -- Status:


 * PM: If A and B commute so do A and B^{-1}, id=7303 -- WP guess: If A and B commute so do A and B^-1 -- Status:


 * PM: Levy-Desplanques theorem, id=7490 -- WP guess: Levy-Desplanques theorem -- Status:


 * PM: linear extension, id=7240 -- WP guess: linear extension -- Status:


 * PM: Neumann Series, id=7277 -- WP guess: Neumann Series -- Status:


 * PM: parameterization of equitable matrices, id=6678 -- WP guess: parameterization of equitable matrices -- Status:


 * PM: proof of Rodrigues' rotation formula, id=7221 -- WP guess: proof of Rodrigues' rotation formula -- Status:


 * PM: Properties of diagonally dominant matrix, id=7483 -- WP guess: Properties of diagonally dominant matrix -- Status:


 * PM: Rodrigues' rotation formula, id=7150 -- WP guess: Rodrigues' rotation formula -- Status:


 * PM: rotation matrix, id=6786 -- WP guess: rotation matrix -- Status:


 * PM: The characteristic polynomial of a orthogonal matrix is a reciprocal polynomial, id=7452 -- WP guess: The  characteristic polynomial of a orthogonal matrix is a reciprocal polynomial -- Status:


 * PM: addition and subtraction formulas for sine and cosine, id=9260new! -- WP guess: addition and subtraction formulas for sine and cosine -- Status:


 * PM: antipodal map on S^n is homotopic to the identity if and only if n is odd, id=7753new! -- WP guess: antipodal map on S^n is homotopic to the identity if and only if n is odd -- Status:


 * PM: compound matrix, id=8326new! -- WP guess: compound matrix -- Status:


 * PM: concavity of sine function, id=9289new! -- WP guess: concavity of sine function -- Status:


 * PM: conformal partitioning, id=8127new! -- WP guess: conformal partitioning -- Status:


 * PM: determinant of anti-diagonal matrix, id=7817new! -- WP guess: determinant of anti-diagonal matrix -- Status:


 * PM: example of linear least squares, id=9102new! -- WP guess: example of linear least squares -- Status:


 * PM: generalized eigenvector, id=9754new! -- WP guess: generalized eigenvector -- Status:


 * PM: geometric derivation of addition formulas for sine and cosine, id=9483new! -- WP guess: geometric derivation of addition formulas for sine and cosine -- Status:


 * PM: linear complex structure, id=8392new! -- WP guess: linear complex structure -- Status:


 * PM: linear least squares fit, id=9776new! -- WP guess: linear least squares fit -- Status:


 * PM: point, id=8173new! -- WP guess: point -- Status:


 * PM: proof of determinant lower bound of a strict diagonally dominant matrix, id=9304new! -- WP guess: proof of determinant lower bound of a strict diagonally dominant matrix -- Status:


 * PM: proof of existence and uniqueness of singular value decomposition, id=9434new! -- WP guess: proof of existence and uniqueness of singular value decomposition -- Status:


 * PM: proof that \det e^A = e^{\operatorname{tr}A}, id=7858new! -- WP guess: proof that \det e^A = e^\operatornametrA -- Status:


 * PM: skew Hadamard matrix, id=8314new! -- WP guess: skew Hadamard matrix -- Status:


 * PM: squeezing \mathbb{R}^n, id=9479new! -- WP guess: squeezing \mathbbR^n -- Status:


 * PM: submatrix notation, id=8325new! -- WP guess: submatrix notation -- Status:

15-01 Instructional exposition (textbooks, tutorial papers, etc.)

 * PM: circulant matrix, id=4640 -- WP: circulant matrix -- Status: A
 * The PM article does have a more general definition, but I have my doubts about it (what if A = {1,2,3,4} and &sigma; = (1 3)(2 4)? ), and there is no reference. -- Jitse Niesen (talk) 23:22, 22 November 2005 (UTC)


 * PM: derivative of inverse matrix, id=6362 -- WP: invertible matrix -- Status: M
 * Added the formula to the WP article, which could use some rigorous editing. -- Jitse Niesen (talk) 00:34, 23 November 2005 (UTC)


 * PM: identity matrix, id=1223 -- WP: identity matrix -- Status: M
 * Merged some (rather trivial) information about eigenvalues and eigenvectors. -- Jitse Niesen (talk) 00:34, 23 November 2005 (UTC)


 * PM: matrix, id=2464 -- WP: matrix (mathematics) -- Status: A
 * Lots of information in both PM and WP article. Articles clearly differ in what information is listed, with WP one being clearly more low-level, but both articles are essentially fine. -- Jitse Niesen (talk) 21:28, 29 November 2005 (UTC)


 * PM: zero matrix, id=5789 -- WP: zero matrix -- Status: A
 * PM article has some more things, but it's all trivial. -- Jitse Niesen (talk) 21:28, 29 November 2005 (UTC)


 * PM: derivative of matrix, id=6713 -- WP guess: derivative of matrix -- Status:


 * PM: isomorphism of rings of real and complex matrices, id=8403new! -- WP guess: isomorphism of rings of real and complex matrices -- Status:

15A03 Vector spaces, linear dependence, rank

 * PM: basis, id=1041 -- WP: basis (linear algebra) -- Status: A
 * Jitse Niesen (talk) 21:28, 29 November 2005 (UTC)


 * PM: complementary subspace, id=3209 -- WP: direct sum of modules -- Status: M
 * I mentioned the term "complementary subspace" in Direct sum of modules. It might be good to make Direct sum of vector spaces in a separate article, because the module stuff is a bit more abstract. -- Jitse Niesen (talk) 15:27, 18 December 2005 (UTC)


 * PM: countable basis, id=1434 -- WP: Schauder basis -- Status: C
 * This definition was hinted at in various places, but I think it can use an article on its own. -- Jitse Niesen (talk) 15:27, 18 December 2005 (UTC)


 * PM: diagonalization of quadratic form, id=6490 -- WP: none -- Status: N
 * I don't think we need an article for this; see diagonalizable matrix and quadratic form. -- Jitse Niesen (talk) 01:27, 20 December 2005 (UTC)


 * PM: dimension (vector space), id=2993 -- WP: dimension (vector space) -- Status: A
 * WP article is actually more complete. -- Jitse Niesen (talk) 01:27, 20 December 2005 (UTC)


 * PM: direct sum of Hermitian and skew-Hermitian matrices, id=4238 -- WP: Hermitian matrix, skew-Hermitian matrix -- Status: A
 * PM article says basically that every matrix can be written as a sum of a Hermitian and a skew-Hermitian matrix, which is already mentioned in the two WP articles. I don't think we need to make more of it . -- Jitse Niesen (talk) 01:27, 20 December 2005 (UTC)


 * PM: Euclidean vector space, id=5743 -- WP: Euclidean space -- Status: A
 * WP article is perfectly adequate. -- Jitse Niesen (talk) 01:27, 20 December 2005 (UTC)


 * PM: every vector space has a basis, id=3494 -- WP: basis (linear algebra) -- Status: A
 * PM includes a proof, using Zorn's lemma, but I don't think we need that. -- Jitse Niesen (talk) 01:27, 20 December 2005 (UTC)

I am here

 * PM: fixed-point subspace, id=4435 -- WP guess: fixed-point subspace -- Status:


 * PM: flag, id=2994 -- WP guess: flag -- Status:


 * PM: frame, id=2931 -- WP guess: frame -- Status:


 * PM: Hamel function, id=5703 -- WP guess: Hamel function -- Status:


 * PM: linear combination, id=805 -- WP guess: linear combination -- Status:


 * PM: linear independence, id=848 -- WP guess: linear independence -- Status:


 * PM: list vector, id=3200 -- WP guess: list vector -- Status:


 * PM: nullity, id=2237 -- WP: nullity -- Status: A
 * Actually, I just made the WP article redirect to null space, which has all the info on PlanetMath and more. Oleg Alexandrov 17:57, 16 May 2005 (UTC)


 * PM: orthonormal basis, id=5346 -- WP guess: orthonormal basis -- Status:


 * PM: physical vector, id=3201 -- WP guess: physical vector -- Status:


 * PM: proof of rank-nullity theorem, id=2361 -- WP guess: proof of rank-nullity theorem -- Status:


 * PM: proof of Riesz' Lemma, id=6627 -- WP guess: proof of Riesz' Lemma -- Status:


 * PM: rank, id=2236 -- WP guess: rank -- Status:


 * PM: rank-nullity theorem, id=2238 -- WP guess: rank-nullity theorem -- Status:


 * PM: Riesz' Lemma, id=6626 -- WP guess: Riesz' Lemma -- Status:


 * PM: scalar, id=870 -- WP guess: scalar -- Status:


 * PM: similar matrix, id=2278 -- WP guess: similar matrix -- Status:


 * PM: span, id=806 -- WP guess: span -- Status:


 * PM: standard basis, id=5806 -- WP guess: standard basis -- Status:


 * PM: Sylvester's law, id=3356 -- WP guess: Sylvester's law -- Status:


 * PM: theorem for the direct sum of finite dimensional vector spaces, id=4233 -- WP guess: theorem for the direct sum of finite dimensional vector spaces -- Status:


 * PM: unit vector, id=865 -- WP guess: unit vector -- Status:


 * PM: vector, id=2909 -- WP guess: vector -- Status:


 * PM: absorbing set, id=7287 -- WP guess: absorbing set -- Status:


 * PM: annihilator of vector subspace, id=7280 -- WP guess: annihilator of vector subspace -- Status:


 * PM: closure of a vector subspace in a normed space is a vector subspace, id=6709 -- WP guess: closure of a vector subspace in a normed space is a vector subspace -- Status:


 * PM: closure of a vector subspace is a vector subspace, id=6710 -- WP guess: closure of a vector subspace is a vector subspace -- Status:


 * PM: complexification of vector space, id=7249 -- WP guess: complexification of vector space -- Status:


 * PM: every finite dimensional proper subspace of a normed space is nowhere dense, id=6687 -- WP guess: every finite dimensional proper subspace of a normed space is nowhere dense -- Status:


 * PM: every finite dimensional subspace of a normed space is closed, id=6686 -- WP guess: every finite dimensional subspace of a normed space is closed -- Status:


 * PM: axiomatization of dependence, id=8621new! -- WP guess: axiomatization of dependence -- Status:


 * PM: blade, id=7994new! -- WP guess: blade -- Status:


 * PM: determining rank of matrix, id=9674new! -- WP guess: determining rank of matrix -- Status:


 * PM: dimension formulae for vector spaces, id=8701new! -- WP guess: dimension formulae for vector spaces -- Status:


 * PM: proof of the dimension theorem for subspaces, id=8782new! -- WP guess: proof of the dimension theorem for subspaces -- Status:


 * PM: rank-nullity theorem, id=8790new! -- WP guess: rank-nullity theorem -- Status:


 * PM: symmetric tensor, id=8369new! -- WP guess: symmetric tensor -- Status:

15A04 Linear transformations, semilinear transformations

 * PM: AB and BA are almost isospectral, id=6386 -- WP guess: AB and BA are almost isospectral -- Status:


 * PM: \operatorname{ker} L=\{0\} if and only if L is injective, id=6384 -- WP guess: \operatornameker L=\0\ if and only if L is injective -- Status:


 * PM: adjoint endomorphism, id=2718 -- WP guess: adjoint endomorphism -- Status:


 * PM: admissibility, id=5448 -- WP guess: admissibility -- Status:


 * PM: affine transformation, id=6413 -- WP guess: affine transformation -- Status:


 * PM: conductor of a vector, id=5455 -- WP guess: conductor of a vector -- Status:


 * PM: cyclic decomposition theorem, id=5449 -- WP guess: cyclic decomposition theorem -- Status:


 * PM: cyclic subspace, id=5447 -- WP guess: cyclic subspace -- Status:


 * PM: cyclic vector theorem, id=5680 -- WP guess: cyclic vector theorem -- Status:


 * PM: dimension theorem for symplectic complement (proof), id=4149 -- WP guess: dimension theorem for symplectic complement (proof) -- Status:


 * PM: double dual embedding, id=2916 -- WP guess: double dual embedding -- Status:


 * PM: dual homomorphism, id=2717 -- WP guess: dual homomorphism -- Status:


 * PM: dual homomorphism of the derivative, id=2842 -- WP guess: dual homomorphism of the derivative -- Status:


 * PM: equivalently oriented bases, id=4928 -- WP guess: equivalently oriented bases -- Status:


 * PM: I-AB is invertible if and only if I-BA is invertible, id=6383 -- WP guess: I-AB is invertible if and only if I-BA is invertible -- Status:


 * PM: image of a linear transformation, id=4530 -- WP guess: image of a linear transformation -- Status:


 * PM: invertible linear transformation, id=1935 -- WP guess: invertible linear transformation -- Status:


 * PM: isospectral, id=6387 -- WP guess: isospectral -- Status:


 * PM: kernel of a linear transformation, id=807 -- WP guess: kernel of a linear transformation -- Status:


 * PM: linear isomorphism, id=6186 -- WP guess: linear isomorphism -- Status:


 * PM: linear transformation, id=697 -- WP guess: linear transformation -- Status:


 * PM: minimal polynomial (endomorphism), id=3615 -- WP guess: minimal polynomial (endomorphism) -- Status:


 * PM: necessary and sufficient condition for diagonalizability, id=5711 -- WP guess: necessary and sufficient condition for diagonalizability -- Status:


 * PM: primary decomposition theorem, id=5707 -- WP guess: primary decomposition theorem -- Status:


 * PM: proof of cyclic vector theorem, id=5690 -- WP guess: proof of cyclic vector theorem -- Status:


 * PM: proof of necessary and sufficient condition for diagonalizability, id=5712 -- WP guess: proof of necessary and sufficient condition for diagonalizability -- Status:


 * PM: self-dual, id=2719 -- WP guess: self-dual -- Status:


 * PM: symplectic complement, id=4139 -- WP guess: symplectic complement -- Status:


 * PM: theorem about cyclic subspaces, id=5702 -- WP guess: theorem about cyclic subspaces -- Status:


 * PM: trace, id=1844 -- WP guess: trace -- Status:


 * PM: unimodular matrix, id=6662 -- WP guess: unimodular matrix -- Status:


 * PM: decomposition of orthogonal operators as rotations and reflections, id=7242 -- WP guess: decomposition of orthogonal operators as rotations and reflections -- Status:


 * PM: dimension of the special orthogonal group, id=7245 -- WP guess: dimension of the special orthogonal group -- Status:


 * PM: linear transformation is continuous if its domain is finite dimensional, id=7098 -- WP guess: linear transformation is continuous if its domain is finite dimensional -- Status:


 * PM: AB is conjugate to BA, id=8045new! -- WP guess: AB is conjugate to BA -- Status:


 * PM: additive function, id=8409new! -- WP guess: additive function -- Status:


 * PM: commuting matrices, id=7906new! -- WP guess: commuting matrices -- Status:


 * PM: determining rotations and reflections in \mathbb{R}^2, id=9572new! -- WP guess: determining rotations and reflections in \mathbbR^2 -- Status:


 * PM: Euclidean transformation, id=8021new! -- WP guess: Euclidean transformation -- Status:


 * PM: permutation operator, id=8368new! -- WP guess: permutation operator -- Status:


 * PM: semilinear transformation, id=7835new! -- WP guess: semilinear transformation -- Status:


 * PM: strain transformation, id=9804new! -- WP guess: strain transformation -- Status:


 * PM: symmetrizer, id=8370new! -- WP guess: symmetrizer -- Status:


 * PM: symmetry, id=9530new! -- WP guess: symmetry -- Status:


 * PM: there exist additive functions which are not linear, id=8417new! -- WP guess: there exist additive functions which are not linear -- Status:

15A06 Linear equations

 * PM: finite-dimensional linear problem, id=2502 -- WP guess: finite-dimensional linear problem -- Status:


 * PM: Gaussian elimination, id=1238 -- WP guess: Gaussian elimination -- Status:


 * PM: homogeneous linear problem, id=2500 -- WP guess: homogeneous linear problem -- Status:


 * PM: linear problem, id=2496 -- WP guess: linear problem -- Status:


 * PM: reduced row echelon form, id=1617 -- WP guess: reduced row echelon form -- Status:


 * PM: row echelon form, id=1616 -- WP guess: row echelon form -- Status:


 * PM: under-determined polynomial interpolation, id=2840 -- WP guess: under-determined polynomial interpolation -- Status:


 * PM: conjugate gradient algorithm, id=6685 -- WP guess: conjugate gradient algorithm -- Status:


 * PM: extended discussion of the conjugate gradient method, id=9859new! -- WP guess: extended discussion of the conjugate gradient method -- Status:


 * PM: general solution of linear differential equation, id=8722new! -- WP guess: general solution of linear differential equation -- Status:

15A09 Matrix inversion, generalized inverses

 * PM: generalized inverse, id=6065 -- WP guess: generalized inverse -- Status:


 * PM: Hilbert matrix, id=3479 -- WP: Hilbert matrix -- Status:


 * PM: matrix adjoint, id=3604 -- WP guess: matrix adjoint -- Status:


 * PM: matrix inverse, id=3483 -- WP guess: matrix inverse -- Status:


 * PM: Moore-Penrose generalized inverse, id=6067 -- WP: Moore-Penrose generalized inverse -- Status:


 * PM: Pascal matrix, id=4445 -- WP guess: Pascal matrix -- Status:


 * PM: Proof of matrix inverse calculation by Gaussian elimination, id=5700 -- WP guess: Proof of matrix inverse calculation by Gaussian elimination -- Status:


 * PM: Toeplitz matrix, id=3482 -- WP: Toeplitz matrix -- Status:


 * PM: invertible matrices are dense in set of nxn matrices, id=7579 -- WP guess: invertible matrices are dense in set of nxn matrices -- Status:


 * PM: group inverse, id=9306new! -- WP guess: group inverse -- Status:


 * PM: inverse of matrix with small-rank adjustment, id=7724new! -- WP guess: inverse of matrix with small-rank adjustment -- Status:


 * PM: proof of inverse of matrix with small-rank adjustment, id=7726new! -- WP guess: proof of inverse of matrix with small-rank adjustment -- Status:

15A12 Conditioning of matrices

 * PM: matrix condition number, id=3480 -- WP: condition number -- Status:


 * PM: singular, id=758 -- WP guess: singular -- Status:


 * PM: matrix condition number is greater or equal to 1, id=7324 -- WP guess: matrix condition number is greater or equal to 1 -- Status:

15A15 Determinants, permanents, other special matrix functions

 * PM: Cauchy-Binet formula, id=5523 -- WP guess: Cauchy-Binet formula -- Status:


 * PM: Cayley-Hamilton theorem, id=1837 -- WP guess: Cayley-Hamilton theorem -- Status:


 * PM: cofactor expansion, id=978 -- WP guess: cofactor expansion -- Status:


 * PM: Cramer's rule, id=626 -- WP guess: Cramer's rule -- Status:


 * PM: determinant, id=2797 -- WP guess: determinant -- Status:


 * PM: determinant as a multilinear mapping, id=3595 -- WP guess: determinant as a multilinear mapping -- Status:


 * PM: determinant condition for a sequence of vectors, id=6116 -- WP guess: determinant condition for a sequence of vectors -- Status:


 * PM: determinants of some matrices of special form, id=5417 -- WP guess: determinants of some matrices of special form -- Status:


 * PM: example of Cramer's rule, id=3169 -- WP guess: example of Cramer's rule -- Status:


 * PM: Hadamard product, id=5706 -- WP guess: Hadamard product -- Status:


 * PM: minor (of a matrix), id=5522 -- WP guess: minor (of a matrix) -- Status:


 * PM: n'th derivative of a determinant, id=6044 -- WP guess: n'th derivative of a determinant -- Status:


 * PM: Pfaffian, id=5857 -- WP guess: Pfaffian -- Status:


 * PM: proof of cofactor expansion, id=3896 -- WP guess: proof of cofactor expansion -- Status:


 * PM: proof of Cramer's rule, id=3462 -- WP guess: proof of Cramer's rule -- Status:


 * PM: proof of the determinant condition for a sequence of vectors, id=6117 -- WP guess: proof of the determinant condition for a sequence of vectors -- Status:


 * PM: resolvent matrix, id=4235 -- WP guess: resolvent matrix -- Status:


 * PM: block determinants, id=7279 -- WP guess: block determinants -- Status:


 * PM: Determinant inequalities, id=7489 -- WP guess: Determinant inequalities -- Status:


 * PM: matrix resolvent properties, id=7468 -- WP guess: matrix resolvent properties -- Status:


 * PM: proof of block determinants, id=7315 -- WP guess: proof of block determinants -- Status:


 * PM: proof of Cayley-Hamilton theorem by formal substitutions, id=7308 -- WP guess: proof of Cayley-Hamilton theorem by formal substitutions -- Status:


 * PM: Schur complement, id=7302 -- WP guess: Schur complement -- Status:


 * PM: Van der Waerden's permanent conjecture, id=6935 -- WP guess: Van der Waerden's permanent conjecture -- Status:


 * PM: basis-free definition of determinant, id=9109new! -- WP guess: basis-free definition of determinant -- Status:


 * PM: determinant in terms of traces of powers, id=7964new! -- WP guess: determinant in terms of traces of powers -- Status:


 * PM: lecture notes on the Cayley-Hamilton theorem, id=9096new! -- WP guess: lecture notes on the Cayley-Hamilton theorem -- Status:


 * PM: proof of Cayley-Hamilton theorem in a commutative ring, id=8106new! -- WP guess: proof of Cayley-Hamilton theorem in a commutative ring -- Status:

15A18 Eigenvalues, singular values, and eigenvectors

 * PM: characteristic equation, id=1838 -- WP guess: characteristic equation -- Status:


 * PM: eigenvalue, id=1496 -- WP guess: eigenvalue -- Status:


 * PM: eigenvalue, id=5106 -- WP guess: eigenvalue -- Status:


 * PM: Jordan canonical form theorem, id=3364 -- WP guess: Jordan canonical form theorem -- Status:


 * PM: Lagrange multiplier method, id=2352 -- WP guess: Lagrange multiplier method -- Status:


 * PM: Perron-Frobenius theorem, id=3812 -- WP guess: Perron-Frobenius theorem -- Status:


 * PM: proof of calculus theorem used in the Lagrange method, id=4073 -- WP guess: proof of calculus theorem used in the Lagrange method -- Status:


 * PM: proof of Jordan canonical form theorem, id=5709 -- WP guess: proof of Jordan canonical form theorem -- Status:


 * PM: spectral theorem, id=3072 -- WP guess: spectral theorem -- Status:


 * PM: algebraic and geometric multiplicity do not coincide, id=7037 -- WP guess: algebraic and geometric multiplicity do not coincide -- Status:


 * PM: common eigenvector of a diagonal element cross-section, id=7378 -- WP guess: common eigenvector of a diagonal element cross-section -- Status:


 * PM: invariance of eigenvalues, id=7087 -- WP guess: invariance of eigenvalues -- Status:


 * PM: proof of Lagrange multiplier method, id=7263 -- WP guess: proof of Lagrange multiplier method -- Status:


 * PM: multiplicity of eigenvalue, id=7036 -- WP guess: multiplicity of eigenvalue -- Status:


 * PM: proof of Wielandt-Hoffman theorem, id=6682 -- WP guess: proof of Wielandt-Hoffman theorem -- Status:


 * PM: Rayleigh-Ritz theorem, id=7546 -- WP guess: Rayleigh-Ritz theorem -- Status:


 * PM: spectrum of A-\mu I, id=7444 -- WP guess: spectrum of A-\mu I -- Status:


 * PM: Wielandt-Hoffman theorem, id=6680 -- WP guess: Wielandt-Hoffman theorem -- Status:


 * PM: eigenspace, id=9752new! -- WP guess: eigenspace -- Status:


 * PM: finding eigenvalues, id=7873new! -- WP guess: finding eigenvalues -- Status:


 * PM: generalized eigenspace, id=9761new! -- WP guess: generalized eigenspace -- Status:

15A21 Canonical forms, reductions, classification

 * PM: companion matrix, id=3773 -- WP guess: companion matrix -- Status:


 * PM: eigenvalues of an involution, id=4301 -- WP guess: eigenvalues of an involution -- Status:


 * PM: example of linear involution, id=5678 -- WP guess: example of linear involution -- Status:


 * PM: linear involution, id=4197 -- WP guess: linear involution -- Status:


 * PM: normal matrix, id=4358 -- WP guess: normal matrix -- Status:


 * PM: projection, id=3208 -- WP: projection (linear algebra) -- Status:


 * PM: proof of theorem for normal matrices, id=7530 -- WP guess: proof of theorem for normal matrices -- Status:


 * PM: simultaneous block-diagonalization of upper triangular commuting matrices, id=7353 -- WP guess: simultaneous block-diagonalization of upper triangular commuting matrices -- Status:


 * PM: simultaneous triangularisation of commuting matrices over any field, id=7352 -- WP guess: simultaneous triangularisation of commuting matrices over any field -- Status:


 * PM: simultaneous upper triangular block-diagonalization of commuting matrices, id=7350 -- WP guess: simultaneous upper triangular block-diagonalization of commuting matrices -- Status:


 * PM: theorem for normal matrices, id=7346 -- WP guess: theorem for normal matrices -- Status:


 * PM: diagonalizable, id=8056new! -- WP guess: diagonalizable -- Status:

15A23 Factorization of matrices

 * PM: matrix factorization, id=5699 -- WP guess: matrix factorization -- Status:


 * PM: QR decomposition, id=1207 -- WP guess: QR decomposition -- Status:


 * PM: commuting matrices are simultaneously triangularizable, id=7294 -- WP guess: commuting matrices are simultaneously triangularizable -- Status:


 * PM: commuting normal matrices are simultaneously diagonalizable, id=7295 -- WP guess: commuting normal matrices are simultaneously diagonalizable -- Status:


 * PM: proof that commuting matrices are simultaneously triangularizable, id=7301 -- WP guess: proof that commuting matrices are simultaneously triangularizable -- Status:

15A30 Algebraic systems of matrices

 * PM: ideals in matrix algebras, id=4767 -- WP guess: ideals in matrix algebras -- Status:


 * PM: characteristic matrix of diagonal element cross-section, id=7354 -- WP guess: characteristic matrix of diagonal element cross-section -- Status:


 * PM: monomial matrix, id=7050 -- WP guess: monomial matrix -- Status:


 * PM: elementary matrix, id=8985new! -- WP guess: elementary matrix -- Status:

15A33 Matrices over special rings (quaternions, finite fields, etc.)

 * PM: proportions of invertible matrices, id=7973new! -- WP guess: proportions of invertible matrices -- Status:

15A36 Matrices of integers

 * PM: permutation matrix, id=1232 -- WP guess: permutation matrix -- Status:


 * PM: example of permutation matrix, id=6771 -- WP guess: example of permutation matrix -- Status:

15A39 Linear inequalities

 * PM: Farkas lemma, id=4508 -- WP guess: Farkas lemma -- Status:


 * PM: proof of Farkas lemma, id=5649 -- WP guess: proof of Farkas lemma -- Status:


 * PM: generalized Farkas lemma, id=9705new! -- WP guess: generalized Farkas lemma -- Status:

15A42 Inequalities involving eigenvalues and eigenvectors

 * PM: Bauer-Fike Theorem, id=6465 -- WP guess: Bauer-Fike Theorem -- Status:


 * PM: Gershgorin's circle theorem, id=3709 -- WP guess: Gershgorin's circle theorem -- Status:


 * PM: Gershgorin's circle theorem result, id=4536 -- WP guess: Gershgorin's circle theorem result -- Status:


 * PM: Shur's inequality, id=4410 -- WP guess: Shur's inequality -- Status:


 * PM: Brauer's ovals theorem, id=7503 -- WP guess: Brauer's ovals theorem -- Status:


 * PM: Minimal Gershgorin set, id=7514 -- WP guess: Minimal Gershgorin set -- Status:


 * PM: Ostrowski theorem, id=7528 -- WP guess: Ostrowski theorem -- Status:


 * PM: proof of Bauer-Fike theorem, id=7450 -- WP guess: proof of Bauer-Fike theorem -- Status:


 * PM: proof of Shur's inequality, id=7501 -- WP guess: proof of Shur's inequality -- Status:


 * PM: proof of Weyl's inequality, id=7464 -- WP guess: proof of Weyl's inequality -- Status:


 * PM: Weyl's inequality, id=7463 -- WP guess: Weyl's inequality -- Status:

15A45 Miscellaneous inequalities involving matrices

 * PM: Hadamard's inequality, id=6084 -- WP guess: Hadamard's inequality -- Status:


 * PM: proof of Hadamard's inequality, id=7541 -- WP guess: proof of Hadamard's inequality -- Status:

15A48 Positive matrices and their generalizations; cones of matrices

 * PM: copositive matrix, id=6197 -- WP: copositive matrix -- Status: A Lunch 00:05, 7 January 2007 (UTC)


 * PM: Euclidean distance matrix, id=6200 -- WP guess: Euclidean distance matrix -- Status:


 * PM: generalized Vandermonde matrix is positive definite, id=6124 -- WP guess: generalized Vandermonde matrix is  positive definite -- Status:


 * PM: negative definite, id=1968 -- WP guess: negative definite -- Status:


 * PM: negative semidefinite, id=1970 -- WP guess: negative semidefinite -- Status:


 * PM: positive definite, id=1967 -- WP guess: positive definite -- Status:


 * PM: positive semidefinite, id=1969 -- WP guess: positive semidefinite -- Status:


 * PM: primitive matrix, id=3809 -- WP guess: primitive matrix -- Status:


 * PM: reducible matrix, id=3810 -- WP guess: reducible matrix -- Status:


 * PM: square root of positive definite matrix, id=7067 -- WP guess: square root of positive definite matrix -- Status:


 * PM: generalized Vandermonde matrix, id=9759new! -- WP guess: generalized Vandermonde matrix -- Status:


 * PM: totally positive matrix, id=9758new! -- WP guess: totally positive matrix -- Status:

15A51 Stochastic matrices

 * PM: Birkoff-von Neumann theorem, id=3610 -- WP guess: Birkoff-von Neumann theorem -- Status:


 * PM: proof of Birkoff-von Neumann theorem, id=3611 -- WP guess: proof of Birkoff-von Neumann theorem -- Status:


 * PM: stochastic matrix, id=2885 -- WP guess: stochastic matrix -- Status:


 * PM: there are no non-square doubly stochastic matrices, id=6938 -- WP guess: there are no non-square doubly stochastic matrices -- Status:


 * PM: eigenvalues of stochastic matrix, id=8421new! -- WP guess: eigenvalues of stochastic matrix -- Status:


 * PM: Google matrix, id=9302new! -- WP guess: Google matrix -- Status:

15A52 Random matrices

 * PM: random vector, id=5974 -- WP guess: random vector -- Status:

15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)

 * PM: Cauchy matrix, id=6050 -- WP guess: Cauchy matrix -- Status:


 * PM: Cayley's parameterization of orthogonal matrices, id=6535 -- WP guess: Cayley's parameterization of orthogonal matrices -- Status:


 * PM: condition of orthogonality, id=6455 -- WP guess: condition of orthogonality -- Status:


 * PM: determinant of the Vandermonde matrix, id=6120 -- WP guess: determinant of the Vandermonde matrix -- Status:


 * PM: eigenvalues of a Hermitian matrix are real, id=5879 -- WP guess: eigenvalues of a Hermitian matrix are real -- Status:


 * PM: Engel's theorem, id=2991 -- WP guess: Engel's theorem -- Status:


 * PM: Givens rotation, id=1215 -- WP guess: Givens rotation -- Status:


 * PM: Hermitian matrix, id=1505 -- WP guess: Hermitian matrix -- Status:


 * PM: Householder transformation, id=1210 -- WP guess: Householder transformation -- Status:


 * PM: skew-Hermitian matrix, id=4231 -- WP guess: skew-Hermitian matrix -- Status:


 * PM: transpose, id=975 -- WP guess: transpose -- Status:


 * PM: Vandermonde matrix, id=3481 -- WP guess: Vandermonde matrix -- Status:


 * PM: M-matrix, id=7257 -- WP guess: M-matrix -- Status:


 * PM: stable matrix, id=7312 -- WP guess: stable matrix -- Status:


 * PM: Z-matrix, id=7255 -- WP guess: Z-matrix -- Status:


 * PM: fully indecomposable matrix, id=7999new! -- WP guess: fully indecomposable matrix -- Status:


 * PM: proof of determinant of the Vandermonde matrix, id=7699new! -- WP guess: proof of determinant of the Vandermonde matrix -- Status:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory

 * PM: Frobenius matrix norm, id=109 -- WP guess: Frobenius matrix norm -- Status:


 * PM: matrix p-norm, id=108 -- WP guess: matrix p-norm -- Status:


 * PM: self consistent matrix norm, id=4310 -- WP guess: self consistent matrix norm -- Status:

15A63 Quadratic and bilinear forms, inner products

 * PM: anti-symmetric, id=2826 -- WP guess: anti-symmetric -- Status:


 * PM: Cauchy-Schwarz inequality, id=1628 -- WP guess: Cauchy-Schwarz inequality -- Status:


 * PM: dot product, id=239 -- WP guess: dot product -- Status:


 * PM: every orthonormal set is linearly independent, id=4169 -- WP guess: every orthonormal set is linearly independent -- Status:


 * PM: inner product space, id=1613 -- WP guess: inner product space -- Status:


 * PM: linearization, id=6580 -- WP guess: linearization -- Status:


 * PM: proof of Cauchy-Schwarz inequality, id=2827 -- WP guess: proof of Cauchy-Schwarz inequality -- Status:


 * PM: proof of Cauchy-Schwarz inequality for real numbers, id=6635 -- WP guess: proof of Cauchy-Schwarz inequality for real numbers -- Status:


 * PM: quadratic form, id=1940 -- WP guess: quadratic form -- Status:


 * PM: skew-symmetric bilinear form, id=3626 -- WP guess: skew-symmetric bilinear form -- Status:


 * PM: Euclidean vector space, id=7571 -- WP guess: Euclidean vector space -- Status:


 * PM: hermitian form over a division ring, id=7626 -- WP guess: hermitian form over a division ring -- Status:


 * PM: invariant scalar product, id=7364 -- WP guess: invariant scalar product -- Status:


 * PM: quadratic space, id=6827 -- WP guess: quadratic space -- Status:


 * PM: unimodular, id=7553 -- WP guess: unimodular -- Status:


 * PM: alternating form, id=7649new! -- WP guess: alternating form -- Status:


 * PM: Gram determinant, id=7637new! -- WP guess: Gram determinant -- Status:


 * PM: hyperbolic pairs and basis, id=7833new! -- WP guess: hyperbolic pairs and basis -- Status:


 * PM: left / right perpendicular, id=8315new! -- WP guess: left / right perpendicular -- Status:


 * PM: orthogonal direct sum, id=7645new! -- WP guess: orthogonal direct sum -- Status:


 * PM: reflexive non-degenerate sesquilinear, id=7834new! -- WP guess: reflexive non-degenerate sesquilinear -- Status:

15A66 Clifford algebras, spinors

 * PM: geometric algebra, id=3770 -- WP guess: geometric algebra -- Status:


 * PM: spinor, id=9366new! -- WP guess: spinor -- Status:


 * PM: twistor, id=9385new! -- WP guess: twistor -- Status:

15A69 Multilinear algebra, tensor products

 * PM: basic tensor, id=2953 -- WP guess: basic tensor -- Status:


 * PM: Einstein summation convention, id=4130 -- WP guess: Einstein summation convention -- Status:


 * PM: multi-linear, id=2796 -- WP guess: multi-linear -- Status:


 * PM: outer multiplication, id=2951 -- WP guess: outer multiplication -- Status:


 * PM: tensor, id=3112 -- WP guess: tensor -- Status:


 * PM: tensor algebra, id=3776 -- WP guess: tensor algebra -- Status:


 * PM: tensor array, id=2949 -- WP guess: tensor array -- Status:


 * PM: tensor product (vector spaces), id=2087 -- WP guess: tensor product (vector spaces) -- Status:


 * PM: tensor transformations, id=2952 -- WP guess: tensor transformations -- Status:


 * PM: coboundary definition of exterior derivative, id=7564 -- WP guess: coboundary definition of exterior derivative -- Status:


 * PM: simple tensor, id=7282 -- WP guess: simple tensor -- Status:


 * PM: tensor product basis, id=7254 -- WP guess: tensor product basis -- Status:


 * PM: second order tensor: symmetric and skew-symmetric parts, id=7847new! -- WP guess: second order tensor: symmetric and skew-symmetric parts -- Status:

15A72 Vector and tensor algebra, theory of invariants

 * PM: bac-cab rule, id=5436 -- WP guess: bac-cab rule -- Status:


 * PM: cross product, id=867 -- WP guess: cross product -- Status:


 * PM: euclidean vector, id=860 -- WP guess: euclidean vector -- Status:


 * PM: mutual positions of vectors, id=6178 -- WP guess: mutual positions of vectors -- Status:


 * PM: rotational invariance of cross product, id=4171 -- WP guess: rotational invariance of cross product -- Status:


 * PM: tensor density, id=6608 -- WP guess: tensor density -- Status:


 * PM: triple cross product, id=5714 -- WP guess: triple cross product -- Status:


 * PM: vector product in general vector spaces, id=6089 -- WP guess: vector product in general vector spaces -- Status:


 * PM: distance of non-parallel lines, id=7304 -- WP guess: distance of non-parallel lines -- Status:


 * PM: dyad product, id=7293 -- WP guess: dyad product -- Status:


 * PM: position vector, id=7265 -- WP guess: position vector -- Status:


 * PM: right-handed system of vectors, id=6704 -- WP guess: right-handed system of vectors -- Status:


 * PM: scalar factor transfer rules, id=7292 -- WP guess: scalar factor transfer rules -- Status:


 * PM: solid angle, id=7266 -- WP guess: solid angle -- Status:


 * PM: direction cosines, id=9615new! -- WP guess: direction cosines -- Status:

15A75 Exterior algebra, Grassmann algebras

 * PM: contraction, id=4261 -- WP guess: contraction -- Status:


 * PM: exterior algebra, id=2819 -- WP guess: exterior algebra -- Status:


 * PM: visualizations of exterior forms, id=7323 -- WP guess: visualizations of exterior forms -- Status:

15A78 Other algebras built from modules

 * PM: symmetric algebra, id=7730new! -- WP guess: symmetric algebra -- Status:

15A90 Applications of matrix theory to physics

 * PM: Matrix Logarithm, id=7394 -- WP guess: Matrix Logarithm -- Status:


 * PM: perspective drawing, id=7628 -- WP guess: perspective drawing -- Status:

15A99 Miscellaneous topics

 * PM: dual space, id=1739 -- WP guess: dual space -- Status:


 * PM: example of trace of a matrix, id=4160 -- WP guess: example of trace of a matrix -- Status:


 * PM: generalized Kronecker delta symbol, id=4119 -- WP guess: generalized Kronecker delta symbol -- Status:


 * PM: Iwasawa decomposition, id=6088 -- WP guess: Iwasawa decomposition -- Status:


 * PM: Kronecker delta, id=1221 -- WP guess: Kronecker delta -- Status:


 * PM: linear functional, id=1608 -- WP guess: linear functional -- Status:


 * PM: modules are a generalization of vector spaces, id=4288 -- WP guess: modules are a generalization of vector spaces -- Status:


 * PM: proof of properties of trace of a matrix, id=4396 -- WP guess: proof of properties of trace of a matrix -- Status:


 * PM: quasipositive matrix, id=3811 -- WP guess: quasipositive matrix -- Status:


 * PM: trace of a matrix, id=930 -- WP guess: trace of a matrix -- Status:


 * PM: an application of Z-matrix in a mobile radio system, id=8339new! -- WP guess: an application of Z-matrix in a mobile radio system -- Status:


 * PM: duality with respect to a non-degenerate bilinear form, id=8528new! -- WP guess: duality with respect to a non-degenerate bilinear form -- Status:


 * PM: spanning sets of dual space, id=9634new! -- WP guess: spanning sets of dual space -- Status: