Splet07. maj 2014 · The SVD approximation theorem The theorem is: Let the SVD of a matrix be (1) B = USVT where S is a diagonal matrix with elements greater than or equal to zero and U and V are orthogonal matrices for real data or unitary for complex data. Let Sr be the S matrix with diagonal entries r + 1 to K set equal to zero. The matrix Br (2) Br = USrVT Spleton why low-rank approximations are useful here, one example may be found in the SVD demo code available on the course website. Here, we discuss the so-called Eckart-Young-Mirsky theorem. This Theorem tells us that A k is the best approximation of Aby a rank kmatrix, in fact it is so in two di erent norms. Theorem 1 (Eckart-Young-Mirsky ...

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