CHARACTERISTICS OF MATRIX SVD AND ITS APPLICATIONS TO RANK DEFICIENCY FREE NETWORK ADJUSTMENT
矩阵的SVD分解性质及其在秩亏网平差中的应用

The matrix SVD(Singular Value Decomposition) and the relation between SVD and Moore-Penrose inverses are analyzed. It is derived that the generalize inverse matrix of SVD is Moore-Penrose generalized inverse of the matrix namely.The relation between the SVD and the minimum norm least squares solution of linear system of equation is also analyzed and the formulas of free network adjustment based on matrix singular value decomposition are presented. The formulas for solving weighted minimum norm least squares are also presented, which expanded the minimum norm least squares solution of linear system of equation based on matrix SVD. The practical computations show that the SVD method is correct and validity in free network adjustment.