线性约束下双反对称矩阵扩充及其最佳逼近

Under the Linear Constraint Anti-bisymmetric Matrix Extension and its Optimal Approximation

首次提出并讨论了一类带有线性约束的双反对称矩阵扩充问题,得到了问题有解的充分必要条件,并给出了解的一般表达式.此外,还给出了解集合中与给定矩阵的最佳逼近解的表达式.

This paper firstly considers a kind of linear constrained matrix extension problems of the anti - bisymmetric matrices. The necessary and sufficient conditions for the existence of and the expression for the general solutions are given. Moreover, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived.