Singular value decomposition and Moore-penrose inverse for unitary extended matrix

Based on the ordinary SVD,a quantitative correspondence of the singular values and singular vectors between the unitary extended matrix and its mother matrix is derived.At the same time,we analysis the quantitative correspondence of F~* and G~*matrices of unitary extended matrices and its mother matrix A, and the Moore-Penrose inverse,e.g.g-inverse,reflected g-inverse,least square g-inverse,least norm g-inverse. Finally,we also give the corresponding algorithms of SVD and maximum rank decomposition for unitary ex- tended matrix and illustrate the applications above theory.Based on,we can save dramatically the CPU time and memory.