The normal matrices are the matrices which are unitarily diagonalizable, i.e.,
is a normal matrix iff there exists a unitary matrix such that is a diagonal matrix.
All Hermitian matrices are normal but have real
eigenvalues, whereas a general normal matrix has no such restriction on its eigenvalues.
All normal matrices are diagonalizable, but not all diagonalizable matrices are normal.

The following table gives the number of normal square matrices of given types for orders ,
2, ....