16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.4.11

Bilinear Forms

Mathematics — Linear Algebra · determinant-preserving-operator

Problem

Let

F

be a subfield of

C

V

a finite-dimensional vector space over

F

, and

f

a non-singular bilinear form on

V

. If

T

is a linear operator on

V

preserving

f

, prove that

\det T = \pm 1