If A is nilpotent to index k , its minimal polynomial is t k . A normal matrix is hermitian iff its eigenvalues are all real. The singular values of a normal matrix are the absolute values of the eigenvalues. The eigenvalues of A H are the conjugates of the eigenvalues of A and have the same eigenvectors. A normal matrix is unitary iff its eigenvalues all have an absolute value of 1.
Orthogonal matrices correspond to rotations and reflections.
Most properties are listed under unitary . A is a permutation matrix if its columns are a permutation of the columns of I . The set of permuation matrices is closed under multiplication and inversion. A permutation matrix is orthogonal . A Toeplitz matrix is persymmetric.