Linear Algebra Done Right · Problem 5D.18

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · diagonalizable-operators

Problem

Suppose that

T \in \mathcal{L}(V)

is diagonalizable and

U

is a subspace of

V

that is invariant under

T

. Prove that the quotient operator

T/U

is a diagonalizable operator on

V/U

. The quotient operator

T/U

was defined in Exercise 38 in Section 5A.