A procedure is reported for the compression of rank-deficient matrices. A matrix A of rank k is represented in the form A = U ∘ B ∘ V, where B is a k× k submatrix of A, and U, V are well-conditioned matrices that each contain a k× k identity submatrix. This property enables such compression schemes to be used in certain situations where the singular value decomposition (SVD) cannot be used efficiently. Numerical examples are presented.
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Cheng et al. (2005) studied this question.
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