Exercise 7.A.8

Answers

Proof. Suppose $S, T \in L (V)$ are self-adjoint. Then

(S + T) = S + T = S^{∗} + T^{∗} = {(S + T)}^{∗},

proving that $S + T$ is self-adjoint. Let $λ \in ℝ$ . Then

(λT) = λT = λ T^{∗} = {(\bar{λ} T)}^{∗} = {(λT)}^{∗},

proving that $λT$ is self adjoint. □

celiopassos

2017-10-06 00:00