Several Specific Solutions Problems Of A Matrix Equation

In this paper, a class of matrix equation AXB = C is discussed. Applying mechanics of partitioning of matrix and special structure, we have given the sufficient and necessary conditions for the matrix if it has bisymmetric and anti-bisymmetric solutions. The expressions of the general solutions are given, in addition the optimal approximate solutions under different circumstance are provided.For generalized bisymmetric and generalized anti-bisymmetric matrix, applying the correlative knowledge of Moore-Penrose inverse and special structure, we have given the sufficient and necessary condition and the expression. Otherwise under specific circumstance, we have considered the generalized anti-bisymmetric least square solution.During the considering of several kinds of specific solutions, we indirectly have given somemethods of resolution and special solutions for the matrix equation A₁X₁B₁ + A₂X₂B₂ = C.