Linear Algebra Done Right · Problem 7F.5

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms

Problem

Suppose UU is a finite-dimensional inner product space, T∈L(V,U)T \in \mathcal{L}(V, U), and S∈L(U,W)S \in \mathcal{L}(U, W). Prove that ∥ST∥≤∥S∥∥T∥.\|ST\| \leq \|S\| \|T\|.

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