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)