Linear Algebra Done Right · Problem 7E.15

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · singular-value-decomposition

Problem

Suppose

T \in \mathcal{L}(V)

and

s_1 \geq \cdots \geq s_n

are the singular values of

T

. Prove that if

\lambda

is an eigenvalue of

T

, then

s_1 \geq |\lambda| \geq s_n