Exercise 7.B.8

Answers

Proof. Let $V$ be a $3$ -dimensional complex vector space and $v_{1}, v_{2}, v_{3}$ a basis for it. Define $T \in L (V)$ by

\begin{aligned} T v_{1} & = v_{2} \\ T v_{2} & = v_{3} \\ T v_{3} & = 0 . \end{aligned}

Obviously $T^{9} = T^{8} = 0$ , however $T^{2} e_{1} = e_{3}$ and $T e_{1} = e_{2}$ , therefore $T^{2} \neq T$ . □

celiopassos

2017-10-06 00:00