Show that the Eigen values of a Hermitian matrix is real.
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Recall that x is an eigenvector, hence x is not the zero vector and the length ||x||≠0. λ=ˉλ. It follows from this that the eigenvalue λ is a real number. Since λ is an arbitrary eigenvalue of A, we conclude that all the eigenvalues of the Hermitian matrix A are real numbers.
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