Linear Algebra Done Right · Problem 5D.2

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · diagonalizable-operators

Problem

Suppose

T \in \mathcal{L}(V)

has a diagonal matrix

A

with respect to some basis of

V

. Prove that if

\lambda \in \mathbf{F}

, then

\lambda

appears on the diagonal of

A

precisely

\dim E(\lambda, T)

times.