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Section 40.3 Terminology and notation

orthogonally diagonalizable

a real square matrix \(A\) for which there exists an orthogonal matrix \(P\) such that \(\inv{P} A P = \utrans{P} A P\) is diagonal

unitarily diagonalizable

a complex square matrix \(A\) for which there exists a unitary matrix \(U\) such that \(\inv{U} A U = \adjoint{U} A U\) is diagonal

normal matrix

a complex square matrix which commutes with its adjoint; i.e. a complex matrix \(A\) for which \(\adjoint{A} A = A \adjoint{A}\)