【摘要】 考虑如下问题: 问题1.给定。记求,使得。 问题2.给定。记,求,使得借助于矩阵分解得出了问题2有解的充分必要条件,给出了问题1与问题2的解的表示。更多还原

【Abstract】 The following problems are considered:Problem 1. Given A∈SR^m×m,B∈SR^n×n,D∈R^m×n.Let S₁= {X|X^m×n,‖AX+BX-D‖=min}, find （?） ∈ S₁,such that ‖（?）‖ = min.Problem 2. Given A∈SR^m×m,B∈SR^n×n,D∈R^m×n. Let S₂={X|X^m×n, AX+BX=D} ,find （?）∈S₂,such that ‖（?）‖= min.By applying matrix decompositions,the necessary and sufficient condition, under which S₂ is nonempty,is studied. The expressions for the solutions of Problem 1 and Problem 2 are given.更多还原