The Anti-Hermite Reflexive Solutions of Matrix Equation
Peng Xiang-yang · Zhongyang Minzu Daxue xuebao · 2006
A n×n complex P is said to be a generalized reflection matrix if P~H=P and P~2=I.A n×n complex X is said to be an anti-Hermite reflexive matrix with respect to the generalized reflection matrix P if X~H=P=-X and X=PXP.By applying the generalized singular value decomposition(GSVD) of matrices,this paper provides the necessary and sufficient conditions for the existence and the expression for the anti-Hermite reflexive with a generalized reflection P solutions of the matrix equation A~HXA=B(A,B∈C~n×n).In addition,in anti-Hermite reflextive solution set of the equation, the expressions of the optimal approximation solution and of the minimum norm solution to the given matrix are derived.