Talk:Shift matrix

Stub status
I've given this article stub status for the simple reason that I have little to say about the application of shift matrices. The article needs more discussion of eigenvalues and eigenvectors and the degeneracy of shift matrices; infinite shift matrices; their relevance to engineering problems etc. Dan Pope 02:58, 10 November 2006 (UTC)

Anita, here is proof that your edits are erroneous
Lets take the 3x3 upper shift matrix and call it U3.

[0,1,0]

[0,0,1]

[0,0,0]

Now we apply this after the following simple matrix we shall designate A:

[1,2,3]

[4,5,6]

[7,8,9]

AU3=

[0,1,2]

[0,3,4]

[0,7,8]

Notice the elements are shifted to the right. — Preceding unsigned comment added by 2001:48f8:29:0:74ae:e60d:6335:4c22 (talk) 19:29, 19 October 2017 (UTC)


 * The real problem is that row vector in the lead should have been column vector, which was confusing. I have now corrected this.  The action on column vectors is as follows:
 * Let
 * $$ v = \begin{pmatrix}

a \\ b \\ c \\ d \\ e \end{pmatrix}. $$
 * Then
 * $$U_5 v = \begin{pmatrix}

0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}\begin{pmatrix} a \\ b \\ c \\ d \\ e \end{pmatrix} = \begin{pmatrix} b \\ c \\ d \\ e \\ 0 \end{pmatrix},$$


 * $$L_5 v = \begin{pmatrix}

0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{pmatrix}\begin{pmatrix} a \\ b \\ c \\ d \\ e \end{pmatrix} = \begin{pmatrix} 0 \\ a \\ b \\ c \\ d \end{pmatrix}.$$
 * — Anita5192 (talk) 00:26, 20 October 2017 (UTC)