矩阵最高阶非零子式的精确定位法  

The Precise Positioning Method of the Highest-order Nonzero Subexpression of the Matrix

作　　者：范飞亚 杨泽辉 龙全贞 FAN Feiya;YANG Zehui;LONG Quanzhen(China Coast Guard Academy,Ningbo,Zhejiang Province,315801 China)

机构地区：[1]武警海警学院,浙江宁波315801

出　　处：《科技资讯》2023年第18期207-210,共4页Science & Technology Information

摘　　要：该文对矩阵的最高阶非零子式进行了探讨,分析了在初等行变换下,矩阵的最高阶非零子式如何变化,进而给出了寻找最高阶非零子式的一种普适算法。从矩阵秩的定义出发,利用初等行变换把一个矩阵化成行阶梯形矩阵;根据行阶梯形矩阵,可以看出原矩阵的最高阶非零子式所在的大致位置;再利用初等行变换的逆变换,逐步定位出原矩阵的最高阶非零子式的精确位置。This paper discusses the highest-order nonzero subexpression of the matrix,analyzes how the highest-order nonzero subexpression of the matrix changes under elementary row transformation,and then gives a universal algorithm to find the highest-order nonzero subexpression.Starting from the definition of the rank of matrix,this paper uses elementary row transformation to transform a matrix into a row ladder matrix,and the approximate position of the highest-order nonzero subexpression of the original matrix can be seen according to the row ladder matrix,and then,it uses the inverse transformation of elementary row transformation to gradually locate the exact position of the highest-order nonzero subexpression of the original matrix.

关 键 词：矩阵的秩 初等行变换 初等变换的逆变换 最高阶非零子式 

分 类 号：O151.21[理学—数学]