Linear Algebra Done Right · Problem 7F.1

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms

Problem

Prove that if S,T∈L(V,W)S, T \in \mathcal{L}(V, W), then ∣∥S∥−∥T∥∣≤∥S−T∥\big|\|S\| - \|T\|\big| \leq \|S - T\|. The inequality above is called the reverse triangle inequality.

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