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Homework Statement
A is a square matrix of size n, B is of size m, C is an m*n(typo,should be n*m) matrix and n>m ,Rank(C)=m.
if AC=CB, prove characteristic polynomial of B divides that of A.
Homework Equations
nothing
The Attempt at a Solution
I think I need to prove any eigenvalue of B is an eigenvalue of A, then prove the multiplicity of any B's eigenvalue is less than or equal to that of A's.
First part is easy to prove, if Bx=[tex]\lambda[/tex] x, then CBx=[tex]\lambda[/tex]Cx=ACx, so [tex]\lambda[/tex] is also an eigenvalue of A, with eigenvector Cx.
Second part, I'm totally stuck
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