Linear Algebra Done Right · Problem 7F.28

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · polar-decomposition

Problem

Suppose T∈L(V)T \in \mathcal{L}(V). Prove that there exists a unitary operator S∈L(V)S \in \mathcal{L}(V) such that T=TT∗ ST = \sqrt{TT^*}\, S.

Related theory

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