Kunze Linear Algebra · Problem 8.5.13

Inner Product Spaces

Mathematics — Methods · normal-operators-polynomial

Problem

Let TT be a normal operator on a finite-dimensional complex inner product space. Prove that there is a polynomial ff, with complex coefficients, such that T∗=f(T)T^* = f(T). (Represent TT by a diagonal matrix, and see what ff must be.)

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