子空间上矩阵方程AX=B的亚正定与亚半正定解  

The Positive Subdefinite and Semipositive Subdefinite Solutions of Matrix Equation AX=B on Subspace

作　　者：袁永新[1] 蒋家尚[1] 

机构地区：[1]华东船舶工业学院基础学科系,江苏镇江212003

出　　处：《工程数学学报》2003年第4期85-89,共5页Chinese Journal of Engineering Mathematics

摘　　要：研究了矩阵方程AX=B在子空间Ω={x∈Rn｜Gx=0,G∈Rk×n}上的亚正定及亚半正定解,给出了解存在的充分必要条件及其通解表达式。The positive subdefinite and semipositive subdefinite solutions of matrix equation AX=B on subspace Ω=｛x∈Rn｜Gx=0,G∈Rk×n｝ are discussed. Necessary and sufficient conditions for the existence of such solutions and their general forms are derived using the generalized inverses of matrices.

关 键 词：亚半正定阵 KRONECKER积 广义逆 亚正定阵 矩阵方程 通解 

分 类 号：O24[理学—计算数学]