Linear Algebra Done Right · Problem 7F.7

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms-metric

Problem

Show that defining d(S,T)=∥S−T∥d(S, T) = \|S - T\| for S,T∈L(V,W)S, T \in \mathcal{L}(V, W) makes dd a metric on L(V,W)\mathcal{L}(V, W). This exercise is intended for readers who are familiar with metric spaces.

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