四川师范大学学报（自然科学版）2017，Vol.40Issue(4)：450-456,7.DOI:10.3969/j.issn.1001-8395.2017.04.004
零和自由半环上的半可逆矩阵
Semi-invertible Matrices over Zero-sum-free Semirings
摘要
Abstract
Over zero-sum-free semirings,we give an example to show that matrix equations AX =B andX + A1B =A2B do not always have the same solutions,where A is a known n × n semi-invertible matrix and B is an unknown n-dimensions column vector,A1 and A2 satisfy I + AA1 =AA2 and I + A1A =A2A-We present some conditions under which the systems AX =B and X + A1B =A2B have the same solutions and give some properties of semi-invertible matrices.Our results extend the scope of the application of matrices.关键词
零和自由半环/交换半环/半可逆矩阵/线性方程组/方程组的解Key words
zero-sum-free semirings/commutative semirings/semi-invertible matrix/system of linear equations/solving systems of equations分类
数理科学引用本文复制引用
龙艳华,王学平..零和自由半环上的半可逆矩阵[J].四川师范大学学报（自然科学版）,2017,40(4):450-456,7.基金项目
国家自然科学基金(11171242)、教育部博士点基金(20105134110002)和四川省杰出青年基金(2011JQ0055) （11171242）
