The cardinality of bases in semilinear spaces over commutative semirings

被引：6

作者：

Shu, Qian-yu ^{[1
]}

Wang, Xue-ping ^{[1
]}

机构：

[1] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 459卷

基金：

中国国家自然科学基金;

关键词：

Commutative semiring; Basis Cardinality; Invertible matrix; INVERTIBLE MATRICES;

D O I：

10.1016/j.laa.2014.06.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the cardinality of a basis in semilinear spaces of n-dimensional vectors over commutative semirings. It first discusses the cardinality of a basis and gives a necessary and sufficient condition that each basis has the same number of elements, which is then used to present the characterizations of bases, by the way, it obtains an equivalent description of an invertible matrix. It finally shows a necessary and sufficient condition that each basis has the same number of elements. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：83 / 100

页数：18

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