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Eigenvalue Eigenvectors of a factorizable diagonalizable matrix

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Eigenvalue of a factorizable matrix

Suppose we have a n-by-n symmetric matrix K which can be factorized in a way, K = H * L * H', where L is a m-by-m diagonal matrix and H is a n-by-m matrix. In addition, let's assume n <= m.

Can we compute the eigen-decomposition of K faster by taking the advantage of this factorization?