PROVING THE EXISTENCE OF A SINGULAR VALUE DECOMPOSITION

Matrix factorization is the algorithm factorizing a matrix into the product of several matrices with particular properties. Before 1960’s, matrix factorization was only used in the linear system analysis, but in the last few decades the quickly developed algorithms of matrix factorizations have been applied to solve a variety of problems, like the regression analysis and information technologies. In this thesis, the theoretical derivation of SVD is presented. And all discussions in this work are confined to the real number realm