Answer to Question #17724 in Algebra for akram

Question

Let A is in the set (C^m*m). be hermitian. An eigenvector of A is a nonzero vector X is in the set C^m such
that Ax = zx for some z is in the set C , the corresponding eigenvalue.

a. Prove that all eigenvalues of A are real.

b. Prove that if x and y are eigenvectors corresponding to distinct eigenvalues then x and y are orthogonal.