矩阵乘积的初等变换术及其应用  

An Algorithm of Elementary Operations on Product of Two Matrices and Its Applications

作　　者：叶海江[1] 安希忠[2] 王增辉[2] 

机构地区：[1]吉林农业科技学院基础部,吉林132101 [2]吉林农业大学信息技术学院,长春130118

出　　处：《大学数学》2005年第4期103-105,共3页College Mathematics

摘　　要：通过矩阵乘法运算的拆行拆列表示,巧妙地绕过初等矩阵,建立了矩阵乘积的初等变换术,进而导出了原来运用初等矩阵才能导出的有关初等变换、逆矩阵、矩阵方程、矩阵等价的若干重要结果.By resting on the “column definition” and “row definition” of the product of two matrices, we established an algorithm of elementary operations on a product of two matrices, avoiding the elementary matrices ingeniously, and then direved a series of the important results about the elementary operations, inverse of a matrix, matrix equations, equivalent matrices and so on. Those results had to be derived by the elementary matrices formerly.

关 键 词：初等变换 初等矩阵 矩阵乘积 初等变换术 

分 类 号：O151.21[理学—数学]