任意体上的矩阵方程[X_(nn),A_(ns),X_(nn)B_(nt)]=[A_(ns),O]  

A MATRIX EQUATION [X_(nn)A_(ns),X_(nn)B_(nt)] =[A_(ns),O]OVER AN ARBITRARY SKEW FIELD

作　　者：王卿文[1] 高伟[2] 

机构地区：[1]昌潍师专数学系,山东潍坊261043 [2]昌潍师专英语系,山东潍坊261043

出　　处：《昌潍师专学报》1999年第2期1-7,共7页Journal of Changwei Teachers College

基　　金：山东省自然科学基金项目(097A02113)

摘　　要：本文研究了任意体上的矩阵方程(Ⅰ)给出了(Ⅰ)的相容的充要条件、通解的显式表示、解的性质及其实用解法,通常意义下的投影矩阵在任意体上也得到了进一步的推广。In this paper we study a matrix equation [XnnAns,XnnBnt] = [Ans,O] over an arbitrary skew field. Necessary and sufficient conditions for solvability,an explicit expression of the general solution, properties of the solutions and a practical solving method of the matrix equation are given. The original projection matrix is also generalized over an arbitrary skew field.

关 键 词：任意体 矩阵方程 投影矩阵 幂等矩阵 基础解阵 

分 类 号：O151.21[理学—数学]