Skew-Hermitian matrix defined:

If the conjugate transpose, A†, of a square matrix, A, is equal to its negative, -A, then A is a skew-Hermitian matrix.

Notes:

1. The main diagonal elements of a skew-Hermitian matrix must be purely imaginary, including zero.

2. The cross elements of a skew-Hermitian matrix are complex numbers having equal imaginary part values, and equal-in-magnitude-but-opposite-in-sign real parts.

Hermitian matrix defined:

If a square matrix, A, is equal to its conjugate transpose, A†, then A is a Hermitian matrix.

Notes:

1. The main diagonal elements of a Hermitian matrix must be real.

2. The cross elements of a Hermitian matrix are complex numbers having equal real part values, and equal-in-magnitude-but-opposite-in-sign imaginary parts.