对称矩阵与正交矩阵的推广及其应用  

A New Generalization of the Symmetric Matrix and Orthogonal Matrix and Their Application

作　　者：郭伟[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2011年第5期449-452,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市教委科技项目(KJ090729)资助

摘　　要：给出O-广义(反)对称矩阵、O-广义正交矩阵的定义,研究了它们的性质及两者之间的关系,特别将正交矩阵的广义Gayley分解推广到了O-广义正交矩阵上;利用两者的关系给出了一种矩阵方程的解及解的表示式,获得了许多新结果.In this paper,the o-generalized（anti） symmetric matrix and o-generalized orthogonal matrix are defined,and their properties and relations are discussed,especially,the generalized Cayley decomposition of orthogonal matrix is extended to o-generalized orthogonal matrix;and by using the relation of the two matrices,the solution of a matrix equation and the expression of the solution are given,and many new results are obtained.

关 键 词：全转置矩阵 O-对称矩阵 O-广义正交矩阵 矩阵方程 解 

分 类 号：O151.21[理学—数学]