Exercise 5.B.14

Answers

Proof. Suppose $V$ is finite-dimensional vector space. Let $v_{1}, \dots, v_{n}$ be a basis of $V$ . Define $T \in L (V)$ by

\begin{aligned} T v_{j} & = v_{j + 1}, for j = 1, \dots, n - 1 \\ T v_{n} & = v_{1} \end{aligned}

$T$ is clearly invertible, but $M (T)$ with respect to same basis only has zeros in the diagonal. □

celiopassos

2017-10-06 00:00