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I am just a bit confused, so:

Is determining eigenvalues of hermitian matrix basically the same as how we determine eigenvalues of real-number matrices?

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Short answer: Yes. Find Characteristic equation and solve. – Tapu Sep 23 '12 at 15:23

The characteristic polynomial of a hermitian matrix has all coefficients real. You can write a companion matrix from these coefficients. The companion matrix is a real matrix.

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