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eigenvalues of matrices or operators

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Eigenvalues and eigenvectors of non-symmetrical tridiagonal matrix

.$$ Is it possible to give analytic expressions for the eigenvalues and eigenvectors of $A$? … Wang et. al [1] show that if the elements on the main diagonal are all 0, the eigenvalues and eigenvectors of $A$ can be expressed in trigonometric functions. Thanks for your answer. …
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