摘要
在交换半环上首先研究矩阵的行列式秩与正、负复合矩阵的一些性质和关系,然后给出行列式秩与广义逆矩阵的一些相关结论,最后分别讨论行列式秩为1的矩阵其g-逆、群逆、M-P逆存在的充分必要条件.
Over commutative semirings,we first study some properties and relations between the determinant rank of a matrix and its positive and negative composite matrices.Then we give some conclusions about the determinant rank of a matrix and its generalized inverse matrix.Finally some necessary and sufficient conditions for the existence of g-inverse,group inverse and M-P inverse of a ma-trix whose determinant rank is one are given.
作者
冯鑫
舒乾宇
FENG Xin;SHU Qianyu(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)
出处
《四川师范大学学报（自然科学版）》
CAS
2023年第4期477-487,共11页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(11271132)。
关键词
交换半环
行列式秩
复合矩阵
广义逆矩阵
commutative semirings
determinant rank
compound matrix
generalized inverse matrix
