Homepage › Solution manuals › Sheldon Axler › Linear Algebra Done Right › Exercise 7.B.9

Exercise 7.B.9

Answers

Proof. Suppose that $T$ is a normal operator on $V$ . Let $e_{1}, \dots, e_{n}$ be an orthonormal basis of $V$ consisting of eigenvalues of $T$ and let $λ_{1}, \dots, λ_{n}$ denote their corresponding eigenvalues. Define $S$ by

S e_{j} = \sqrt{λ_{j}} e_{j},

for each $j = 1, \dots, n$ . Obviously, $S^{2} e_{j} = λ_{j} e_{j} = T e_{j}$ . Therefore $S^{2} = T$ . □

celiopassos

2017-10-06 00:00

Exercise 7.B.9

Answers

Comments

Add answer