Kunze Linear Algebra · Problem 4.3.5

Polynomials

Mathematics — Methods · polynomial-similar-matrices

Problem

Let nn be a positive integer and FF a field. Suppose AA is an n×nn \times n matrix over FF and PP is an invertible n×nn \times n matrix over FF. If ff is any polynomial over FF, prove that f(P−1AP)=P−1f(A)P.f(P^{-1}AP) = P^{-1}f(A)P.

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