16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.5.13
Inner Product Spaces
Mathematics — Linear Algebra · normal-operators-adjoint-polynomial
Problem
Let T be a normal operator on a finite-dimensional complex inner product space. Prove that there is a polynomial f, with complex coefficients, such that T∗=f(T). (Represent T by a diagonal matrix, and see what f must be.)