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Feb 3, 2013 at 22:38 history edited Denis Serre CC BY-SA 3.0
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Feb 3, 2013 at 22:36 comment added Denis Serre @Qingyun. This is a correct conclusion. I'll edit accordingly.
Feb 2, 2013 at 23:21 comment added Qingyun I see, as a corollary of your conclusion, there is no solution if $n$ is not dividing the size of matrices, and $xA+yB$ will have distinct eigenvalues if $n$ equal to the size of matrices, are I right?
Feb 2, 2013 at 7:36 comment added Denis Serre Your question is crystal clear. Because of algebraicity, it is the same as to assume that the identity be satsfied for every $(x,y)$ away from $\Sigma$.
Feb 1, 2013 at 19:29 comment added Qingyun Sorry for not making the question clear, I am looking for matrices $A,B$ such that the identity holds for all $x,y$. I guess my terminology is incorrect.
Feb 1, 2013 at 9:32 history answered Denis Serre CC BY-SA 3.0