线性流形上矩阵方程AX=B的一类反问题  

A Class of Inverse Problems of Matrix Equation AX = B on the Linear Manifold

作　　者：袁永新[1] 

机构地区：[1]江苏科技大学数理系,镇江212003

出　　处：《工程数学学报》2005年第2期317-322,共6页Chinese Journal of Engineering Mathematics

摘　　要：设SE={A∈Rn×n|||AY-Z||=min;Y,Z∈Rn×p},Ω={zΩRn|Gz=o,GΩRk×n},R≥Ωn×n={A∈Rn×n|zTaZ≥0,(?)Z∈Ω}考虑问题P:给定X,BΩRn×m,找A∈SE∩R≥Ωn×n使得AX=B。本文给出了问题P有解的充分必要条件,并在有解时,给出了通解的表示。Let SE = {A ∈ Rn × n|||AY - Z|| = min; Y, Z ∈ Rn × p},Ω = {z Ω Rn|Gz = o, G Ω Rk × n},R≥Ω n × n= {A∈R n × n|zTaZ≥0,(?)Z∈Ω} This paper considers the problem P: Given X, B Ω Rn × m,find A ∈SE∩R≥Ω n × n such that AX = B. The necessary and sufficient condition for the existence of a solution to problem P is studied, the expressions for general solutions of the Probleni P are given.

关 键 词：亚半正定矩阵 线性流形 反问题 

分 类 号：O241.6[理学—计算数学]