Consider a matrix A with N orthonormal eigenvectors {xi} and eigenvalues {λi}. Construct the matrix S from the eigenvectors of A as S = [x1    x2    · · ·    xN], where each column of S is an eigenvector of A. Because S is constructed from a set of linearly independent vectors, the inverse matrix S−1 exists. Show that the matrix A' = S†AS is diagonal, and A'ij = λiδij.

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