Linear Algebra Done Right · Problem 9C.15

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · determinants

Problem

Suppose

V

is an inner product space and

T \in \mathcal{L}(V)

. Use the polar decomposition to give a proof that

|\det T| = \sqrt{\det(T^*T)}

that is different from the proof given earlier (see 9.60).