[1]刘一瑾,吴 莉,王学平*.交换半环上矩阵I+XY的正行列式|I+XY|+与负行列式|I+XY|-关系的一个注记[J].四川师范大学学报(自然科学版),2019,(05):579-582.[doi:10.3969/j.issn.1001-8395.2019.05.002]
 LIU Yijin,WU Li,WANG Xueping.Note on the Relations of the Positive/Negative Determinants |I+XY| over Commutative Semirings[J].Journal of SichuanNormal University,2019,(05):579-582.[doi:10.3969/j.issn.1001-8395.2019.05.002]
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交换半环上矩阵I+XY的正行列式|I+XY|+与负行列式|I+XY|-关系的一个注记()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年05期
页码:
579-582
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
Note on the Relations of the Positive/Negative Determinants |I+XY| over Commutative Semirings
文章编号:
1001-8395(2019)05-0579-04
作者:
刘一瑾1 吴 莉2 王学平1*
1.四川师范大学 数学科学学院, 四川 成都 610066; 2.阿坝师范大学 数学与计算机科学学院, 四川 成都 623002
Author(s):
LIU Yijin1 WU Li2 WANG Xueping1
1.College of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan; 2.College of Mathematics and Computer Science, Aba Teachers University, Wenchuan 623002, Sichuan
关键词:
交换半环 矩阵 行列式
Keywords:
commutative semiring matrix determinant
分类号:
O159
DOI:
10.3969/j.issn.1001-8395.2019.05.002
文献标志码:
A
摘要:
研究交换半环上矩阵I+XY的正行列式|I+XY|+与负行列式|I+XY|-的关系,回答文献(Poplin P L, Hartwig R E.Linear Algebra Appl,2004,387:99-132.)中提出的一个开问题.
Abstract:
In this paper, the relations of the positive/negative determinants |I+XY| over commutative semirings are investigated.We give an answer to the open question raised by literature(P.L.Poplin and R.E.Hartwig.Linear Algebra Appl.,2004,387:99-132.).

参考文献/References:

[1] 北京大学数学系几何与代数教研室代数组.高等代数[M].北京:高等教育出版社,1988.
[2] MCDONALD B R.Linear Algebra over Commutative Rings[M].New York:Marcel Dekker,1984.
[3] TAN Y J.On invertible matrices over antirings[J].Linear Algebra Appl,2007,423:428-444.
[4] TAN Y J.On the invertible matrices over commutative semirings[J].Linear and Multilinear Algebra,2013,61:710-724.
[5] KUNTZMAN J.Théorie des Réseaaux Graphes[M].Paris:Dunod(Libraire),1972.
[6] PERFILIEVA I, KUPKA J.Kronecker-capelli theorem in semilinear spaces[C]//RUAN D, LI T R, XU Y, et al.Computational Intelligence:Foundations and Applications.Chengdu:World Scientific,2010:43-51.
[7] WANG X P, SHU Q Y.Bideterminant and rank of matrix[J].Soft Computing,2014,18:729-742.
[8] SHU Q Y, WANG X P.The applications of the bideterminant of a matrix over commutative semirings[J].Linear and Multilinear Algebra,2017,65:1462-1478.
[9] POPLIN P L, HARTWIG R E.Determinantal identities over commutative semiring[J].Linear Algebra Appl,2004,387:99-132.
[10] GOLAN J S.Semirings and Their Applications[M].Dordrecht:Kluwer,1999.

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备注/Memo

备注/Memo:
收稿日期:2017-11-22 接受日期:2018-01-08
基金项目:国家自然科学基金(61573240)
*通信作者简介:王学平(1965—),男,教授,博导,主要从事不确定性数学、格理论、半环上线性代数等的研究,E-mail:xpwang1@hotmail.com
更新日期/Last Update: 2019-07-15