[1]张廷海,甘爱萍.Min-Algebra上矩阵的μ值[J].江西师范大学学报(自然科学版),2013,(03):225-228.
 ZHANG Ting-hai,GAN Ai-ping.The Value of μ of Matrices over the Min-Algebra[J].,2013,(03):225-228.
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Min-Algebra上矩阵的μ值()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2013年03期
页码:
225-228
栏目:
出版日期:
2013-05-01

文章信息/Info

Title:
The Value of μ of Matrices over the Min-Algebra
作者:
张廷海;甘爱萍
江西师范大学数学与信息科学学院,江西南昌,330022
Author(s):
ZHANG Ting-hai;GAN Ai-ping
关键词:
min-algebra列秩极大列秩线性相关线性无关
Keywords:
min-algebrarankcolumn rankmaximal column ranklinearly dependentlinearly independent
分类号:
O151.21
文献标志码:
A
摘要:
利用矩阵理论研究了一类特殊的半环-(Rmin,⊕,(×),∞)上的矩阵的秩、列秩和极大列秩之间的关系,得到了对于min-algebra上任意m×n矩阵,使这3类秩相等的最大整数,即矩阵的μ值的所有情形,扩展了已有的相关结论.
Abstract:
The relationships between the rank,column rank and maximal column rank of matrices over a special semiring-(Rmin,,,∞)are investigated by the theory of matrices.The largest integers of the three types of ranks equaling for all m by n matrices over the min-algebra are obtained.So the related results are extended.

参考文献/References:

[1] Beasley L B,Pullman N J.Semiring rank versus column rank [J].Linear Algebra Appl,1988,101(1):33-48.
[2] Beasley L B,Song S Z.A comparison of nonnegative real ranks and their preservers [J].Linear and Multilinear Algebra,1992,31(1/2/3/4):37-46.
[3] Song S Z.Linear operators that preserve column rank of Boolean matrices [J].Proceedings of the American Mathematical Society,1993,119(4):1085-1088.
[4] Hwang S G,Kim S J,Song S Z.Linear operators that preserve maximal column rank of Boolean matrices [J].Linear and Multilinear Algebra,1994,36(4):305-313.
[5] Song S Z,Yang S D,Hong S M,et al.Linear operators preserving maximal column ranks of nonbinary Boolean matrices [J].General Algebra and Application 2000,20(2):255-265.
[6] Beasley L B,Guterman A E.Rank inequalities over semiring [J].J Korean Math Soc,2005,42(2):223-241.
[7] Song S Z,Kang K T.Rank and perimeter preserver of rank-1 matrices over max algebra [J].Discuss Math Gen Algebra Appl,2003,23(2):125-137.
[8] Kang K T,Song S Z,Beasley L B.Linear preservers of term ranks of matrices over semiring [J].Linear Algebra Appl,2012,436(7):1850-1862.
[9] Song S Z.On spanning column rank of matrices over semirings [J].Bull Korean Math Soc,1995,32(2):337-342.
[10] 任苗苗,邵勇,赵宪忠.保持两类特殊半环上矩阵{1}-逆的线性算子 [J].西北大学学报:自然科学版,2012,42(1):7-11.
[11] 秦松,甘爱萍.加法半群为半格的半环上Green-关系 [J].江西师范大学学报:自然科学版,2012,36(2):151-154.

备注/Memo

备注/Memo:
国家自然科学基金(11261021)
更新日期/Last Update: 1900-01-01