[1]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,(04):450-456.[doi:10.3969/j.issn.1001-8395.2017.04.004 ]
 Semi-invertible Matrices over Zero-sum-free SemiringsLONG Yanhua,WANG Xueping.Semi-invertible Matrices over Zero-sum-free Semirings[J].Journal of SichuanNormal University,2017,(04):450-456.[doi:10.3969/j.issn.1001-8395.2017.04.004 ]
点击复制

零和自由半环上的半可逆矩阵()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2017年04期
页码:
450-456
栏目:
基础理论
出版日期:
2017-04-30

文章信息/Info

Title:
Semi-invertible Matrices over Zero-sum-free Semirings
文章编号:
1001-8395(2017)04-0450-07
作者:
龙艳华1 王学平2*
1. 成都大学 师范学院, 四川 成都 610106;
2. 四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
Semi-invertible Matrices over Zero-sum-free SemiringsLONG Yanhua1 WANG Xueping2
1. College of Teachers, Chengdu University, Chengdu 610016, Sichuan;
2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
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O153.1
Keywords:
zero-sum-free semirings commutative semirings semi-invertible matrix system of linear equations solving systems of equations
分类号:
O153.1; O159
DOI:
10.3969/j.issn.1001-8395.2017.04.004
文献标志码:
A
摘要:
在零和自由半环上,举例说明矩阵方程组AX=B和X+A1B=A2B并不是在所有情况下都同解,其中A是已知的n×n阶半可逆矩阵,X是未知的n维列向量,A1和A2分别满足条件I+AA1=AA2和I+A1A=A2A.得到关于方程AX=B和X+A1B=A2B同解的一些条件,完善零和自由半环上半可逆矩阵的相关性质,扩展矩阵的应用范围.
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.

参考文献/References:

[1] BROUWER R K. A method of relational fuzzy clustering based on producing feature vectors using fast map[J]. Info Sci,2009,179(20):3561-3582.
[2] CAO Z Q, KIM K H, ROUSH F W. Incline Algebra and Applications[M]. New York:Ellis Horwood,1984.
[3] GHAZINOORY S, ESMAIL ZADEH A, KHEIRKHAH A S. Application of fuzzy calculations for improving portfolio matrices[J]. Info Sci,2010,180(9):1582-1590.
[4] GIVE'ON Y. Lattice matrices[J]. Info Control,1964,7(4):477-484.
[5] GONDRAN M, MINOUX M. Graphs Dioïds and Semirings[M]. New York:Springer-Verlag,2008.
[6] KIM K H, ROUSH F W. Generalized fuzzy matrices[J]. Fuzzy Sets and Systems,1980,4(3):293-315.
[7] NOBUHARA H, TRIEU D B K, MARUYAMA T, et al. Max-plus algebra-based wavelet transforms and their FPGA implementation for image coding[J]. Info Sci,2010,180(17):3232-3247.
[8] XU Z. A method based on distance measure for interval-valued intuitionistic fuzzy group decision making[J]. Info Sci,2010,180(1):181-190.
[9] ZHAO X Z, JUN Y B, REN F. The semiring of matrices over a finite chain[J]. Info Sci,2008,178(17):3443-3450.
[10] BACCELLI F L, MAIRESSE I. Ergodic theorems for stochastic operators and discrete event networks[J]. Idempotency,1995,11:171-208.
[11] CUNINGHAME-GREEN R A. Minimax Algebra, Lecture Notes in Economics and Mathematical Systems[M]. Berlin:Springer-Verlag,1979.
[12] GOLAN J S. Semirings and Their Applications[M]. Dordrecht:Kluwer Academic Publishers,1999.
[13] GONDRAN M, MINOUX M. Linear algebra in dioids:a survey of recent results[J]. North-Holland Mathematics Studies,1984,95(8):147-163.
[14] GONDRAN M, MINOUX M. Dioids and semirings:links to fuzzy sets and other applications[J]. Fuzzy Sets and Systems,2007,158(12):1273-1294.
[15] ZIMMERMANN U. Linear and combinatorial optimization in ordered algebraic structures[J]. Bull Am Math Soc,1985,12(1):148-150.
[16] LUCE R D. A note on Boolean matrix theory[J]. Proc Am Math Society,1952,3(3):382-388.
[17] RUTHERFORD D E. Inverses of Boolean matrices[J]. Proc Glasgow Math Association,1963,6(1):49-53.
[18] REUTENAUER C, STRAUBING H. Inversion of matrices over a commutative semiring[J]. J Algebra,1984,88(2):350-360.
[19] ZHAO C K. Inverses of L-fuzzy matrices[J]. Fuzzy Sets and Systems,1990,34(1):103-116.
[20] HAN S C, LI H X. Invertible incline matrices and Cramer's rule over inclines[J]. Lin Alg Appl,2004,389(1):121-138.
[21] TAN Y J. On invertible matrices over antirings[J]. Lin Alg Appl,2007,423(2):428-444.
[22] CECHLROV K, PLVKA J. Linear independence in bottleneck algebras[J]. Fuzzy Sets and Systems,1996,77(77):337-348.
[23] CUNINGHAME-GREEN R A, BUTKOVIC P. Bases in max-algebra[J]. Lin Alg Appl,2004,389(1):107-120.
[24] BEASLEY L R B, PULLMAN N J. Linlnear operators strongly preserving idem, pot, ent matrices over semirings[J]. Lin Alg Appl,1988,99(99):199-216.
[25] GHOSH S. Matrices over semirings[J]. Info Sci,1995,90(1/4):221-230.
[26] PERFILIEVA I, KUPKA J. Kronecker-Capelli Theorem in Semilinear Spaces[M]. Computational Intelligence:Foundations and Applications,2015:43-51.
[27] WEINERT H J. Über Halbringe and Halbkörper Ⅲ[J]. Acta Mathematica Hungarica,1964,15(1):177-194.

备注/Memo

备注/Memo:
收稿日期:2015-06-08
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)
*通信作者简介:王学平(1965—),男,教授,主要从事不确定性的数学理论、格理论和半环上线性代数理论等方面的研究,E-mail:xpwang1@hotmail.com
更新日期/Last Update: 2017-04-30