Research On J-centrosymmetrices Matrix Equation Inverse Problem

By exploiting the structure and reducible property of J -centrosymmetric matrices and J -skew centrosymmetric matrices, the generic solution and the least-squares solution of J - centrosymmetric ( J -skew centrosymmetric) matrix equations are considered in this paper. Also, the problem for the best approximation in solution set of matrix equations to a given matrix is also discussed, and the unique best approximation is presented.The problems which will be mainly discussed in the M.S thesis are as follows: Problemâ… Given X , B a J -centrosymmetrices matrix such that Problemâ…¡Given X , B ,find a J -centrosymmetrices matrix such that Problemâ…¢Let S E be the solution set of Problemâ… or Problemâ…¡.Given _fi n dA'〔S₅ u eh thatProblemâ…£Given X , B ,find a J -skew centrosymmetrices matrix such that Problemâ…¤Given X , B ,find a J -skew centrosymmetrices matrix such thatProblemâ…¥Let S Ebe the solution set of Problemâ…£or Problemâ…¤.Given A^∈C^2m×2m,find A^∈SEsuch that...