用分块法降阶计算行列式和矩阵求秩算法的探讨

An Approach to the Algorithm for Calculating Determinant and Rank of Matrix by the Method of Partitioning and Descending Order

文献[1]提出了用分块法降阶计算高阶行列式和矩阵求秩的方法,但计算量还很大。本文提出两个基本命题,根据行列式或矩阵元素的特点,通过初等变换,进行合理分块,利用基本命题改进算法,使计算量最少。

The literature[1] listed below this article is proposes an algorithm for calculating a higher order determinant and rank of matrix by the method of partitioning and descending order, but this method needs a lot of calculation. In this artide, two basic propositions are presented, and the algorithm is improved to reduce calculation to minimum by way of elementary transformation, reasonable partitioning and descending order.