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

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.