Linear Algebra Done Right · Problem 18

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · inner-products

Problem

Suppose

u_1, \ldots, u_m

is a linearly independent list in

V

. Show that there exists

v \in V

such that

\langle u_k, v \rangle = 1

for all

k \in \{1, \ldots, m\}