Exercise 10.A.6

Answers

Proof. Choose $V = ℝ^{2}$ and define $T \in L (V)$ by

T (x, y) = (- y, x) .

Then

T^{2} (x, y) = (- x, - y),

which shows that $- 1$ is the only eigenvalue of $T^{2}$ , with multiplicity $2$ . Thus $trace (T^{2}) = - 2$ . □

celiopassos

2017-10-06 00:00