It is needed in the preparation of survey of methods for self-adjointness like Hamiltonian operator, Laplacian operator, etc.
Nice question
I think the only one is if the matrices are identity or symmetric positive definite. For Hilbert Operator theory you may follow http://web.math.ku.dk/~durhuus/MatFys/MatFys4.pdf
Thanks, Mr. Joseph Shomberg
Thanks, Mr. Muhammad Ali for your answer.
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