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Exercise 5.C.5

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Proof. Suppose $T$ is diagonalizable. It is easy to see that, for every $λ \in ℂ$ , $T - λI$ is also diagonalizable, because $M (T - λI)$ equals $M (T)$ with the entries on the diagonal subtracted by $λ$ . By Exercise 1, this implies that

V = null (T - λI) \oplus range (T - λI) .

Conversely, suppose (1) holds. (to be continued) □

celiopassos

2017-10-06 00:00

Exercise 5.C.5

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