交换半环上的广义正交矩阵  

The Generalized Orthogonal Matrices over Commutative Semirings

作　　者：刘丽娟 舒乾宇 LIU Lijuan;SHU Qianyu(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2020年第6期747-755,共9页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11401410)。

摘　　要：研究交换半环上广义正交矩阵及有限生成半模中标准正交集的扩充问题.首先,讨论广义正交矩阵的性质;在一定条件下,给出广义正交矩阵的等价刻画;随后,给出存在标准基的有限生成半模中标准正交集扩充为标准正交基的充要条件.In this paper,the generalized orthogonal matrix and extending orthogonal subsets of finitely generated semimodules over a commutative semiring are investigated.First,we investigate some properties of the generalized orthogonal matrix and give the equivalent conditions of the generalized orthogonal matrix under some additional conditions.Then we obtain some necessary and sufficient condition that every standard orthogonal set can be extended to a standard orthogonal basis for finitely generated semimodules.

关 键 词：广义正交矩阵 标准正交集 过渡矩阵 

分 类 号：O153[理学—数学]