Talk:Jordan matrix

article title not in lead sentence

The Wikipedia Manual of Style recommends that the article title appear in the lead sentence.

--Jtir 15:29, 20 September 2006 (UTC)

relationship with Jordan normal form

What is the relationship between this article and the article on the Jordan normal form? --Jtir 08:29, 24 September 2006 (UTC)

This is a little odd and I agree the article should address it. I think of the Jordan normal form as something that applies to matrices over algebraically closed fields (so matrix has a spectrum of eigenvalues, the Jordan form of any matrix exists through conjugation, etc). This article seems to be about formal matrices over arbitrary rings.

The first weird thing I saw was the lead paragraph that says "in the mathematical discipline of matrix theory...". I never heard of such a discipline and was going to change "matrix theory" to "linear algebra". I thought that matrices were a topic from linear algebra. But linear algebra is the study of vector spaces, which are structures over fields, while again this article talks about matrices over rings. That would create matrices for which no Jordan form (through change of coordinates) exists. The article matrix (mathematics) also alludes to matrices over rings but doesn't say anything about them. Can someone clarify? 67.117.147.249 (talk) 02:19, 20 July 2009 (UTC)

ODE's

The section on ODE's doesn't mention one of the more basic characteristics of Jordan blocks, which is that a block of size k gives rise to a solution term of the form $t^{k-1}e^{at}$ or something like that. These powers of t don't occur in the "usual" case where the matrix is diagonalizeable. Maybe I'll see if I can update the article. 67.117.147.249 (talk) 02:23, 20 July 2009 (UTC)

Functions of matrices

@Anita5192: the $f(J_{\lambda ,n})$ matrix should be a function of $\lambda$. The form you reverted back to the article is only true for $\lambda =0$. For example, for $f(A)=A$ the diagonal would be equal to $\lambda$, not $a_{0}=0$. If you want to keep it as it is, the $\lambda =0$ property should be specified somewhere. adamant.pwn — contrib/talk 00:47, 25 July 2021 (UTC)

I just reverted my revert of your deletion. At first I thought the $a_{i}$ were just general elements of a matrix $A$, but now I see they are elements of the series mentioned earlier, and the matrix was not, in general, correct.—Anita5192 (talk) 02:05, 25 July 2021 (UTC)