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Hello everybody There is a nice classical result in linear algebra: if A, B $A, B$ are two matrices in M_n(k), $M_n(k),$ where k $k$ is a filedfield, and B $B$ commutes with every element of M_n(k) $M_n(k)$ which commutes with A, $A$, then $B = f(A) f(A)$ for some polynomial f(x) $f(x)$ in k[x].$k[x].$ I was wondering if anybody knows any (important) theorem which is proved using this result. Thank you.
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Hello everybody There is a nice classical result in linear algebra: if A, B are two matrices in M_n(k), where k is a filed, and B commutes with every element of M_n(FM_n(k) which commutes with A, then B = f(A) for some polynomial f(x) in k[x]. I was wondering if anybody knows any (important) theorem which is proved using this result. Thank you. |
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Looking for applications of a nice result in linear algebraHello everybody There is a nice classical result in linear algebra: if A, B are two matrices in M_n(k), where k is a filed, and B commutes with every element of M_n(F) which commutes with A, then B = f(A) for some polynomial f(x) in k[x]. I was wondering if anybody knows any (important) theorem which is proved using this result. Thank you.
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