Question: Let A Cmxm be hermitian. An eigenvector of A is a nonzero vector x Cm such that Ax = Ax for some A E

Let A Cmxm be hermitian. An eigenvector of A is a nonzero vector x Cm such that Ax = Ax for some A E C, the corresponding eigenvalue. %3D (a) Prove that all eigenvalues of A are real. (b) Prove that if r and y are eigenvectors corresponding to distinct eigenvalues, then r and y are orthogonal.

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