(12) Let T be a diagonalizable linear operator on V-finite dimensional, and let m be any positive integer. Prove that T and Tm are simultaneously diagonalizable.

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(12) Let T be a diagonalizable linear operator on V-finite dimensional, and let m be any
positive integer. Prove that T and Tm are simultaneously diagonalizable.
Transcribed Image Text:(12) Let T be a diagonalizable linear operator on V-finite dimensional, and let m be any positive integer. Prove that T and Tm are simultaneously diagonalizable.
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