4. Show that AE Cnxn is Hermitian and only if iA is skew-Hermitian. Deduce that the eigenvalues of a skew-Hermitian matrix are all pure imaginary and that the eigenvalues of the square of a skew-Hermitian matrix are real and nonpositive.
4. Show that AE Cnxn is Hermitian and only if iA is skew-Hermitian. Deduce that the eigenvalues of a skew-Hermitian matrix are all pure imaginary and that the eigenvalues of the square of a skew-Hermitian matrix are real and nonpositive.
