16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.1.12
Bilinear Forms
Mathematics — Linear Algebra · linear-operators-from-bilinear-forms
Problem
Let f, g be bilinear forms on a finite-dimensional vector space V. Suppose g is non-singular. Show that there exist unique linear operators T1, T2 on V such that
f(α,β)=g(T1α,β)=g(α,T2β)
for all α,β.