CAJ | 학술논문

给定两个广义反射矩阵P，Q，通常对于矩阵方程AX=B关于P，Q的自反解和反自反解的研究大多是通过矩阵分解或广义奇异值分解来进行的。采用广义逆，建立该方程存在自反解和反自反解的充要条件以及解的一般表达式，并研究与之相关的矩阵最佳逼近问题。
급정량개엄의반사구진P，Q，통상대우구진방정AX=B관우P，Q적자반해화반자반해적연구대다시통과구진분해혹엄의기이치분해래진행적。채용엄의역，건립해방정존재자반해화반자반해적충요조건이급해적일반표체식，병연구여지상관적구진최가핍근문제。
Generally, the main methods to study the P, Q reflexive and anti-reflexive solutions of the matrix equa?tion AX=B are the decomposition of matrices and the generalized singular value decomposition of matrices. This paper studies the equation by using the generalized inverse and establishes conditions for the existence and repre?sentations of the reflexive and anti-reflexive solutions .Moreover, the optimal approximation solutions are also dis?cussed.