行列式的映射定义及其几个性质的证明  

The Mapping Definition of Determinant and the Proof of Its Several Properties

作　　者：宁群[1] 刘钢 杜玉霞[1] 

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《宿州学院学报》2012年第11期12-14,28,共4页Journal of Suzhou University

基　　金：宿州学院质量工程项目"线性代数精品课程"(szxyjpkc200905)

摘　　要：给出了行列式的映射定义,并利用初等矩阵与初等变换之间的关系,证明了矩阵乘积的行列式等于它们各自行列式的乘积;三角形矩阵的行列式等于它对角元素的乘积;矩阵A转置的行列式等于A的行列式;设A=(aij)n×n∈Mn(F),Aij是detA中元素aij的代数余子式,则ai1Aj1+ai2Aj2+…+ainAjn={detA i=j 0The paper gives the mapping definition of determinant and by using the relationship between the ele-mentary matrix and the elementary transformation proves that the determinant of matrix product is equal to the product of their respective determinant,triangular matrix determinant is equal to the product of its diagonal ele-ments, and supposing, A=（aij）axn∈Mn（F）,is eofaetor of aij in detA, then ai1Aj1＋ai2Aj2＋…＋ainAjn={0 i≠j^detA i=j

关 键 词：行列式 行列式的性质 初等变换 初等矩阵 

分 类 号：O151.21[理学—数学]