16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.2.18

Bilinear Forms

Mathematics — Linear Algebra · self-dual-basis

Problem

Let

V

be a finite-dimensional vector space over

C

and

f

a non-degenerate symmetric bilinear form on

V

. Prove that there is a basis

\mathfrak{B}

V

such that

\mathfrak{B}' = \mathfrak{B}

. (See Exercise 13 for a definition of

\mathfrak{B}'