摘要
1.引言 用C^(n×m)表示所有n×m阶复矩阵的集合,R^(n×m)表示所有n×m阶实矩阵的集合,R_r^(n×m)表示R^(n×m)中矩阵秩为r的子集.任取A,B∈R^(n×m)。
In this paper, the following problems are considered. Problem Ⅰ. Determine n×n real matrices A and B in AX - BY = Z, whereX,Y and Z are given n×m real matrices. Problem Ⅱ. Determine n×n real matrices A and B in‖(A,B) - (A,B)‖ = inf ?(A,B)∈S_(AB) ‖(A,B) - (A, B)‖where A and B are given n×n real matrices, and S_(AB) is the set of solutions toProblem Ⅰ. The necessary and sufficient conditions for the solubility of Problem Ⅰ and itsgeneral solutions are presented. The existence and uniqueness of the solution to Pro-blem Ⅱ are studied. A practical procedure for computing A and B is provided. The-se results are applied to solve a class of inverse generalized eigenvalue problem. Twonumerical examples are given.
出处
《计算数学》
CSCD
北大核心
1989年第1期29-37,共9页
Mathematica Numerica Sinica
