行反正交矩阵的一些性质  

Some Properties of Contrary Orthogonal Matrix

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,成都610039

出　　处：《重庆工商大学学报（自然科学版）》2012年第2期23-27,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：西华大学应用数学校重点学科(ZXD0910-09-1)项目

摘　　要：给出行反正交矩阵的概念,并讨论其行列式、可逆性、迹、特征值等问题,得到行反正交矩阵的行列式、逆矩阵、特征值与迹;并得出了以下主要结果:行反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;行反正交矩阵的转置矩阵以及它的行转置和列转置矩阵都仍是行反正交矩阵;行反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.This paper gives the concept of contrary orthogonal matrix, discusses determinant, reversibility, trace, eigenvalue and so on, and obtains determinant, inverse matrix, eigenvalue and trace of contrary orthogonalmatrix, meanwhile, draws the conclusion that contrary orthogonal matrix is a symmetric matrix of ranks, that itself, its row transposed matrix and its column transposed matrix are invertible, that the transposed matrix of contraryorthogonal matrix and its row transposed matrix and its column transposed matrix are also contrary orthogonal matrix, that inverse matrix of row transposed matrix of contrary orthogonal matrix is equal to its row transposition ofits inverse matrix, that the inverse matrix of its column transposed matrix is equal to its column transposition of its inverse matrix, that the transition of its row transposed matrix is equal to the row transposition of its transposedmatrix and that the transposition of its column transposed matrix is equal to the column transposition of its transposed matrix.

关 键 词：正交矩阵 行反正交矩阵 行列对称矩阵 

分 类 号：O151.21[理学—数学]