Kunze Linear Algebra · Problem 10.2.9

Bilinear Forms

Mathematics — Methods · diagonal-basis-symmetric-bilinear-form

Problem

Let

f

be a symmetric bilinear form on

R^n

. Use the result of Exercise 8 to prove the existence of an ordered basis

\mathfrak{B}

such that

[f]_{\mathfrak{B}}

is diagonal.