16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.4.13

Bilinear Forms

Mathematics — Linear Algebra · preserving-modified-bilinear-form

Problem

Let

g

be a non-singular bilinear form on a finite-dimensional vector space

V

. Suppose

T

is an invertible linear operator on

V

and that

f

is the bilinear form on

V

given by

f(\alpha, \beta) = g(\alpha, T\beta)

. If

U

is a linear operator on

V

, find necessary and sufficient conditions for

U

to preserve

f