16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.4.7

Elementary Canonical Forms

Mathematics — Linear Algebra · diagonalizable-annihilated-distinct-roots

Problem

Let TT be a linear operator on a finite-dimensional vector space over the field of complex numbers. Prove that TT is diagonalizable if and only if TT is annihilated by some polynomial over CC which has distinct roots.

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