Talk:Commuting matrices

Commute

The lede refers to commutation, but the link does not show any mathematical meaning for commute. Is there a better way to link it? —Preceding unsigned comment added by Throwaway85 (talk • contribs) 10:08, 1 December 2009 (UTC)

Oops – ’twas a link to a disambiguation page.

I’ve fixed it to link to commutativity, which was the intention. Thanks!

—Nils von Barth (nbarth) (talk) 01:22, 3 December 2009 (UTC)

Choose an eigenbasis

The theorem by Frobenius is not stated clearly in the text. Moreover, I presume this needs additional hypotheses: what if one of the matrix does not admit an eigenbasis (see Jordan form)?--Fph 09:51, 3 March 2010 (UTC) —Preceding unsigned comment added by Fph (talk • contribs)

Right, and moreover the statement once corrected becomes a trivial consequence of simultaneous triangularizability. Since apparently nobody is reading this anyway, I'm being bold and will reduce the second paragraph to its bare core. — Preceding unsigned comment added by Marc van Leeuwen (talk • contribs) 07:41, 14 September 2013 (UTC)

Unitarily triangulizable?

The article currently says commuting complex matrices are unitarily simultaneously triangularizable. This is nonsense since general complex matrices are not unitarily triangularizable in the first place (and they always commute with themselves). I'm removing this silly sentence. Also it said that if of two commuting matrices just one is diagonalisable then so it the other, in contradiction to what the Jordan-Chevalley decompostion says; I've corrected that as well. While I'm at it, I'll refine the statement of when the centraliser of A is C[A] to the better description of having equal minimal and characteristic polynomial. — Preceding unsigned comment added by Marc van Leeuwen (talk • contribs) 07:31, 14 September 2013 (UTC)

If a matrix is square, it can be triangularized by Schur decomposition, no? D4nn0v (talk) 23:17, 2 November 2019 (UTC)

Necessary and Sufficient Condition

This paper seems to give a way to find whether two matrices commute or not. It seems relevant to me, though I'm not an expert. I don't want to put it in here if it doesn't belong, so I'm looking for a second opinion? 2001:630:301:A152:0:0:0:29 (talk) 16:36, 26 November 2018 (UTC)

The article cannot be used as being WP:original research. In fact, it is published in a predatory journal, without any reliable referee process, and there is no WP:secondary source allowing to decide whether it is notable.

Also, for such an elementary subject that has been studied during centuries, it is sure that if the results in this article are correct and useful, then they are known for a long times. D.Lazard (talk) 18:56, 26 November 2018 (UTC)

References