Talk:Commuting matrices

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Commute

Latest comment: 15 years ago2 comments2 people in discussion

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)Reply

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)Reply

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)

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.