Linear Algebra Done Right · Problem 6C.14

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · riesz-representation

Problem

Suppose that

e_1, \ldots, e_n

is an orthonormal basis of

V

. Explain why the dual basis (see 3.112) of

e_1, \ldots, e_n

e_1, \ldots, e_n

under the identification of

V'

with

V

provided by the Riesz representation theorem (6.58).