Homepage › Solution manuals › Sheldon Axler › Linear Algebra Done Right › Exercise 7.C.3

Linear Algebra Done Right

Exercise 7.C.3

Answers

Proof. For all $u \in U$ , we have

⟨ T |_{U} u, u ⟩ = ⟨ Tu, u ⟩ = ⟨ u, Tu ⟩ = ⟨ u, T |_{U} u ⟩ .

Thus, $T |_{U}$ is self-adjoint. Furthermore,

⟨ T |_{U} u, u ⟩ = ⟨ Tu, u ⟩ \geq 0,

which shows that $T |_{U}$ is positive. □

celiopassos

2017-10-06 00:00

Comments