A square matrix A is a normal matrix if [A, A^H] = A A^H - A^H A = 0, where [a, b] is the commutator and A^H denotes the conjugate transpose. For example, the matrix [i | 0 0 | 3 - 5i] is a normal matrix, but is not a Hermitian matrix. A matrix m can be tested to see if it is normal in the Wolfram Language using NormalMatrixQ[m]. Normal matrices arise, for example, from a normal equation.

conjugate transpose | diagonalizable matrix | diagonal matrix | Hermitian matrix | normal equation | unitary matrix