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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.
== Necessary and Sufficient Condition ==
This paper <ref>https://www.hindawi.com/journals/mpe/2009/650970/abs/</ref> 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?
[[Special:Contributions/2001:630:301:A152:0:0:0:29|2001:630:301:A152:0:0:0:29]] ([[User talk:2001:630:301:A152:0:0:0:29|talk]]) 16:36, 26 November 2018 (UTC)
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