K-行正交矩阵的一些性质  

Some Properties of the K-Row Orthogonal Matrices

作　　者：贾书伟[1] 何承源[1] 

机构地区：[1]西华大学数学与计算机学院,四川成都610039

出　　处：《安庆师范学院学报（自然科学版）》2011年第4期97-100,共4页Journal of Anqing Teachers College(Natural Science Edition)

基　　金：西华大学应用数学校重点学科(NO.ZXD0910-09-1)项目资助

摘　　要：给出k-行正交矩阵的概念,讨论其行列式、可逆性、迹、特征值等问题,得到k-行正交矩阵的行列式、逆矩阵、特征值与迹,得出了以下主要结果:k-行正交矩阵是行列对称矩阵,它本身以及它的行转置和列转置矩阵都是可逆矩阵;k-行正交矩阵的转置矩阵以及它的行转置和列转置矩阵仍都是k-行正交矩阵;k-行正交矩阵的行转置矩阵的逆矩阵等于其逆矩阵的行转置,其列转置矩阵的逆矩阵等于其逆矩阵的列转置;它的行转置矩阵的转置等于其转置矩阵的行转置,它的列转置矩阵的转置等于其转置矩阵的列转置。We introduce the concept of K-row orthogonal matrix and discuss its determinant,reversibility,trace,elgenvalue problems.Then we obtain the following results that K-row orthogonal matrix is ranks of the symmetric matrix,which itself and its transpose rows and columns transposed matrix is invertible;all transpose matrix of K-row orthogonal matrix,and its transpose rows and columns transposed matrix are still k-row orthogonal matrix;K-row orthogonal matrix transpose matrix of rows is equal to the inverse matrix transpose,the columns transposed matrix of columns equal to the inverse matrix transpose;its row transpose a matrix is equal to the transposed matrix transpose row,its column transpose a matrix is equal to its transposed matrix transpose columns.

关 键 词：矩阵 正交矩阵 k-行正交矩阵 行列对称矩阵 

分 类 号：O151.21[理学—数学]