Abstract
This paper begins by identifying a problem related to the solvability of the matrix equation AX=B, particularly within the realm of generalized centrosymmetric matrices. It exploits the distinctive properties inherent in generalized centrosymmetric matrices, primary focus involves investigating their solutions within the context of the matrix equation AX=B. This paper establishes the necessary and sufficient conditions for solvability while formulating a comprehensive expression for the generalized centrosymmetric solution. Furthermore, the paper delves into addressing the associated optimal approximation quandary concerning a specified matrix within the solution set.
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