The reflexive and anti-reflexive solutions of the matrix equation AHXB=C

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摘要

In this paper, the necessary and sufficient conditions for the solvability of matrix equation AHXB=C over the reflexive or anti-reflexive matrices are given, and the general expression of the solution for a solvable case is obtained. Moreover, the relative optimal approximation problem is considered. The explicit expressions of the optimal approximation solution and the minimum norm solution are both provided.

论文关键词：15A24,Reflexive matrix,Anti-reflexive matrix,Matrix equation,Optimal approximation matrix,Minimum norm solution

论文评审过程：Received 10 June 2005, Revised 19 October 2005, Available online 7 March 2006.

论文官网地址：https://doi.org/10.1016/j.cam.2006.01.024