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Exercise 8.C.1

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Proof. Because

4 = \dim ℂ^{4} = \dim G (3, T) + \dim G (5, T) + \dim G (8, T),

it follows that the multiplicities of the eigenvalues of $T$ are at most $2$ . Thus $p (z) = {(z - 3)}^{2} {(z - 5)}^{2} {(z - 8)}^{2}$ is a polynomial multiple of the characteristic polynomial. Therefore, we must have $p (T) = 0$ . □

celiopassos

2017-10-06 00:00

Exercise 8.C.1

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