a complex linear algebra problem.

Extra Credit. This problem involves complex conjugation. A matrix is said to be skew-symmetric if its transpose is its negative: QT = Q. Imitating the proof of the fact that the eigenvalues of a real symmetric matrix are real, prove: (a) The eigenvalues of real skew-symmetric matrices are purely imaginary (b) The determinant of a real shew-symmetric n x a matrix is non-negative for all n, and zero for n odd. (c) The eigenvalues of real orthogonal matrices lie on the unit circle