(a) Prove that every eigenvalue of a Hermitian matrix A, satisfying AT = as in Exercise 3.6.49. is real.
(b) Show that the eigenvectors corresponding to distinct eigenvalues are orthogonal under the Hermitian dot product on Cn.
(c) Find the eigenvalues and eigenvectors of the following Hermitian matrices, and verify orthogonality:

Transcribed Image Text:

2 2 0i0 i2 i 0 i 2.1 0.1 0