Linear Algebra Done Right · Problem 6C.11

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · orthogonal-projections

Problem

Suppose

T \in \mathcal{L}(V)

and

U

is a finite-dimensional subspace of

V

. Prove that

U \text{ is invariant under } T \iff P_U T P_U = T P_U.