安徽大学学报（自然科学版）2011，Vol.35Issue(4)：1-7,7.
一类约束矩阵方程的可解条件与最佳逼近问题
The solvability conditions for a kind of constrained matrix equation and relevant optimal approximate problem
摘要
Abstract
By use of the decomposition theory of a space and the singular value decomposition of a matrix, some necessary and sufficient conditions for the solvability of the matrix equation AX+ BY = Z in matrix set Crn×n(P,Q) × Can×n(P,Q) are provided, the general representation of the solutions is derived for a solvable case. The expression of the solution for the corresponding optimal approximation problem is given anda perturbation of the solution (A,B) is analyzed.关键词
广义自反矩阵/广义反自反矩阵/约束矩阵方程/最佳逼近Key words
generalized reflexive matrix/ generalized anti-reflexive matrix/constrained matrix equation/optimal approximation分类
数理科学引用本文复制引用
王学锋,张忠志..一类约束矩阵方程的可解条件与最佳逼近问题[J].安徽大学学报（自然科学版）,2011,35(4):1-7,7.基金项目
国家自然科学基金资助项目(10971058) （10971058）
