Linear Algebra Done Right · Problem 7E.14

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · singular-value-decomposition

Problem

Suppose

T \in \mathcal{L}(V, W)

. Let

s_n

denote the smallest singular value of

T

. Prove that

s_n \|v\| \leq \|Tv\|

for every

v \in V