Linear Algebra Done Right · Problem 7C.14

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · positive-operators

Problem

Suppose

T

is a positive operator on

V

and

v_1, \ldots, v_m \in V

. Prove that

\sum_{j=1}^{m} \sum_{k=1}^{m} \langle Tv_k, v_j \rangle \geq 0.