# Matrix Theory Normal Functions

Prove that A is normal if and only if A-A^* and A+A^* commute.

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/linear-transformation/matrix-theory-normal-functions-2ir#### Solution Preview

... is diagonal. Suppose , then . Since is a unitary matrix, then . Now is also diagonal. So and commutes. Thus , then we have

.

Thus ...