16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.3.11

Inner Product Spaces

Mathematics — Linear Algebra · self-adjoint-operators

Problem

Let

V

be a finite-dimensional inner product space, and let

E

be an idempotent linear operator on

V

, i.e.,

E^2 = E

. Prove that

E

is self-adjoint if and only if

EE^* = E^*E