A First Course in Linear Algebra · Problem T22

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · unitary-matrices-eigenvalues

Problem

Suppose that

U

is a unitary matrix with eigenvalue

\lambda

. Prove that

\lambda

has modulus 1, i.e.\

|\lambda| = 1

. This says that all of the eigenvalues of a unitary matrix lie on the unit circle of the complex plane.