Singular Value Decomposition

The singular value decomposition is a factorization of a matrix into . A vector is first rotated by an angle β via , then is scaled by a diagonal matrix to form . Finally the vector is rotated by an angle ω to form .

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Note that U and V are orthogonal matrices and thus do not alter the length of the vectors. In 2D the diagonal matrix Σ has the form
here are the singular values of the matrix.
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