Discover Linear Algebra

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 $\adjoint{A} A = A \adjoint{A}$