16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 9.2.6

Operators on Inner Product Spaces

Mathematics — Linear Algebra · non-degenerate-forms

Problem

Call the form

f

(left) non-degenerate if

0

is the only vector

\alpha

such that

f(\alpha, \beta) = 0

for all

\beta

. Let

f

be a form on an inner product space

V

. Prove that

f

is non-degenerate if and only if the associated linear operator

T_f

(Theorem 1) is non-singular.