16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.1.7

Inner Product Spaces

Mathematics — Linear Algebra · inner-products

Problem

Let

( \ | \ )

be the standard inner product on

C^2

. Prove that there is no nonzero linear operator on

C^2

such that

(\alpha|T\alpha) = 0

for every

\alpha

C^2

. Generalize.