User:Rogério Brito/Books/Loose Topics in Linear Algebra

Topics in Linear Algebra

 * Some basics


 * Cauchy%E2%80%93Schwarz inequality
 * Steinitz exchange lemma
 * Rank (linear algebra)
 * Trace (linear algebra)
 * Trace inequality
 * Change of basis
 * Orthogonal complement
 * Projection (linear algebra)
 * Transpose


 * Rank-nullity theorem


 * Rank%E2%80%93nullity theorem


 * Up to the Spectral Theorem


 * Eigenvalues and eigenvectors
 * Eigendecomposition of a matrix
 * Defective matrix
 * Spectral theorem
 * Characteristic polynomial
 * Cayley%E2%80%93Hamilton theorem
 * Minimal polynomial (linear algebra)


 * Pseudo-inverse


 * Moore%E2%80%93Penrose inverse
 * Proofs involving the Moore%E2%80%93Penrose inverse


 * Factorizations


 * LU decomposition
 * QR decomposition
 * Rank factorization
 * Eigendecomposition of a matrix
 * Cholesky decomposition
 * Singular value decomposition
 * Polar decomposition


 * Transposes and Dual spaces


 * Transpose of a linear map
 * Bilinear form
 * Quadratic form


 * Definiteness of a matrix


 * Definiteness of a matrix
 * Square root of a matrix
 * Square root of a 2 by 2 matrix


 * Other spaces


 * Dual space
 * Direct sum of modules
 * Quotient space (linear algebra)


 * Special matrices


 * Symmetric matrix
 * Hermitian matrix
 * Normal matrix


 * Diagonalizable matrix


 * Skew-symmetric matrix
 * Orthogonal matrix


 * Extra topics in Linear Algebra


 * Determinant
 * Eigenvalue algorithm
 * Rayleigh quotient
 * Schur complement
 * Perron%E2%80%93Frobenius_theorem


 * Extra topics in General


 * Lagrange multiplier
 * Isomorphism theorems
 * Zassenhaus lemma
 * Correspondence theorem (group theory)


 * Spectral Graph Theory


 * Adjacency matrix
 * Incidence matrix
 * Laplacian matrix
 * Algebraic connectivity
 * Cheeger constant (graph theory)


 * Applications of Spectral Graph Theory
 * Spectral clustering
 * Expander graph
 * Cayley graph
 * Kirchhoff's theorem