中心主子矩阵约束下矩阵反问题X^TAX=B的双对称解及其最佳逼近

INVERSE PROBLEM X^TAX=B OF BISYMMETRIC MATRICES SOLUTIONS WITH A CENTER PRINCIPAL SUBMATRIX CONSTRAINT AND ITS OPTIMAL APPROXIMATION

文章研究了中心主子矩阵约束下矩阵方程X^TAX=B的双对称解.利用子空间的基将约束问题转化为非约束问题的方法,得到了有解的充分必要条件及解的一般表达式.进而,考虑了与之相关的任意给定矩阵的最佳逼近问题.

This paper considers the bisymmetric matrices solutions of matrix equations XTAX = B for A under a central principal submatrix constraint. By the basis vectors of subspace, the constraint problem is transformed into a unconstraint problem, and necessary and sufficient conditions for the solvability and the general expression of the solutions are obtained. Moreover, we also obtain the expression of the solution to the related optimal approximation problem.