16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 9.2.9
Operators on Inner Product Spaces
Mathematics — Linear Algebra · non-degenerate-forms-adjoint
Problem
Let f be a non-degenerate form on a finite-dimensional space V. Show that each linear operator S has an 'adjoint relative to f,' i.e., an operator S′ such that f(Sα,β)=f(α,S′β) for all α,β.