Exercise 7.C.2

Answers

Proof. $T$ is the positive square root of $T^{2}$ . Note that

T^{2} v = TTv = Tw = v

hence $v$ is an eigenvalue of $T^{2}$ . From the proof of 7.36, we see that $Tv = \sqrt{1} v$ . But $Tv = w$ , therefore $v = w$ . □

celiopassos

2017-10-06 00:00