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

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.