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I hope this is the forum to ask this question.
We all know that the eigenvectors of a Hermitian operator form an orthonormal basis. But is the opposite true as well. Are the vectors of an orthonormal basis always the eigenvectors of some Hermitian operator? Or do we need added restrictions to make it so, such as an inner product and dual spaces being the complex conjugate of the normal space? Thanks.
We all know that the eigenvectors of a Hermitian operator form an orthonormal basis. But is the opposite true as well. Are the vectors of an orthonormal basis always the eigenvectors of some Hermitian operator? Or do we need added restrictions to make it so, such as an inner product and dual spaces being the complex conjugate of the normal space? Thanks.