Exercise 9.A.10

Answers

Proof. Choose $λ \in ℂ$ such that $λ^{2} + λ + 1 = 0$ and define $T \in L (ℂ^{7})$ by

Tv = λv

for all $v \in ℂ^{7}$ . Then

(T^{2} + T + I) v = T^{2} v + Tv + Iv = (λ^{2} + λ + 1) v = 0 .

Therefore $T^{2} + T + I$ is nilpotent. □

celiopassos

2017-10-06 00:00