非齐次线性方程组的半正解

Semi-Positive Solutions to Non-Homogeneous Linear Equations

线性方程组的不带负分量的非零解向量称为半正解.本文给出非齐次线性方程组AX= b (b≠0)的半正解结构,进而得到该类线性方程组有半正解的充分条件和必要条件以及唯一半正解的充要条件.

Nonzero solution vectorw ithoutnegative com ponentto linearequationsis called its sem i-posi- tive solution. In this article, w e give the structure ofsem i-positive solutionsofnonhom ogeneouslinear equa- tions AX= b (b≠0). Further, w e obtain the sufficientconditions and necessary conditions thatthe linear e- quations has sem i-positive solution and necessary and sufficientcondition thatithasa uniquesem i-positive so- lution.