Linear Algebra Done Right · Problem 6C.7

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · orthogonal-projections

Problem

Suppose that

X

and

Y

are finite-dimensional subspaces of

V

. Prove that

P_X P_Y = 0

if and only if

\langle x, y \rangle = 0

for all

x \in X

and all

y \in Y