选主元换基迭代算法

Algorithm of pivot selection and the Change of base and iteration

本文用换基迭代的思想对初等变换法进行改进.改进后的算法,只需用初等变换求逆的计算量便可同步求出任一矩阵的秩、向量间的线性关系以及一个最高阶可逆子阵及其逆.若矩阵之间有相同向量,利用本算法可使求逆计算大为简化.

In this paper, based on the theory of the change of base and iteration, the method of elementary operation is improved. By the improved method, the rank of any matrix,the linear relation of vectors,the highest order invertible submatrix and its inverse can be given in the mean time, the quantity of which is the quantity of inverse matrix worked out only by the elementary operation.To matrixes with same vectors,the quantity of obtainning inverse matrix can be far reduced this way.