16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.5.6
Inner Product Spaces
Mathematics — Linear Algebra · normal-operators-classification
Problem
Let T be a normal operator on a finite-dimensional complex inner product space. Prove that T is self-adjoint, positive, or unitary according as every characteristic value of T is real, positive, or of absolute value 1. (Use Theorem 22 to reduce to a similar question about diagonal matrices.)