奇异矩阵分解的记录列方法及其应用

Method of Record-column for the Decomposition of Singular and Its Applications

本文首次提出了奇异矩阵分解的记录列方法。该方法可以容易地将任一奇异矩阵A分解为一列满秩阵与一行满秩阵的乘积,因而能直接得到一个恰好包含A的全体非零特征值的非奇异阵D,使特征矩阵的行列式计算降至最低阶,以减少计算工作量。最后将该方法推广到列不满秩的高矩阵(即行数大于列数)的情形,给出了亏秩平差计算中的一个实例。

This paper proposes a method of record-column for decomposition of singular matrix. The method for every singular matrix A has a simple decomposition into the product of a column full rank matrix and a row full rank matrix. Therefore, we can correctly obtain a nonsingular matrix D only containing whole non-zero eigenvalues of A, so that the calculations for its determinant of eigenmatrix may decrease to the lowest order, and the computational quantities may be reduced. Finally, the method is extended to the case of high-matrix (when the row number is greater than the column number) for column non-full ranks, and the example in the computation of adjustments of rank-defect is given.