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 .
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.