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1、矩阵方程的自反和反自反矩阵解 矩阵方程 的自反和反自反矩阵解 摘要：如果 满足条件：（1） ，（2） ，则称 为广义反射矩阵，广义反射矩阵也是自伴的对合矩阵。设 和 都是广义反射矩阵，如果 满足 ，则称 为关于矩阵对 的广义（反）自反矩阵；如果 满足 ，则 称为关于矩阵 的广义（反）自反矩阵。这篇论文介绍了矩阵方程 ，在系数矩阵 ， 为广义（反）自反矩阵的条件下，（反）自反矩阵解存在的充分必要条件及表达形式。另外，研究了矩阵方程 的（反）自反矩阵解集 ，利用矩阵的分解，导出（反）自反矩阵问题的最佳逼近解。关键词：自反矩阵;反自反矩阵;矩
2、阵方程;Frobenius范数;矩阵最佳逼近问题The reflexive and anti-reflexive solutions of thematrix equation Abstract :An complex matrix is said to be a generalized reflection matrix if and .An complex matrix ia said to be a reflexive (or anti-refl
3、exive) matrix with respect to the generalized reflection matrixs , if . An complex matrix ia said to be a reflexive (or anti-reflexive) matrix with respect to the generalized reflection matrix , if .This paper establishes the necessary and suffic
4、ient conditions for the existence of and the expressions for the reflexive and anti-reflexive with respect to a generalized reflection matrixs solutions of the matrix equation .In addition, incorresponding solution set of the equation.The explicit expression of the nearest matrix to a given matrix in the Frobenius noum have been provided.Keywords:Reflexive matrix; Anti-reflexive matrix; Matrix equation; Frobenius norm; Matrix nearness problem.