Linear Algebra Done Right · Problem 8B.19

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · characteristic-polynomial-unitary

Problem

Suppose

\mathbf{F} = \mathbf{C}

and

S \in \mathcal{L}(V)

is a unitary operator. Prove that the constant term in the characteristic polynomial of

S

has absolute value 1.