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零和自由半环上可逆矩阵的一些性质

, PP. 25-30

Keywords: 交换半环,零和自由半环,可逆矩阵,对角矩阵

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Abstract:

讨论零和自由半环上矩阵可逆的性质.首先给出半环上矩阵可逆的充要条件和可逆矩阵的基本形式,证明了可逆矩阵经过有限次乘方后是一个可逆的对角矩阵,然后证明了可逆矩阵与其转置矩阵的乘积由一些置换矩阵乘以矩阵的转置与矩阵的积来表示,最后讨论了矩阵的双行列式以及矩阵不可逆的充分条件.

References

[1]  Cuninghame-Green R A. Minimax Algebra, Lecture Notes in Economics and Mathematical Systems[M]. Berlin:Springer-Verlag,1979.
[2]  Golan J S. Semirings and Their Applications[M]. Dordrecht:Kluwer Academic Publishers,1999.
[3]  Gondran M, Minoux M. Linear algebra in dioids: a survey of recent results[J]. Ann Discrete Math,1984,19:147-164.
[4]  Gondran M, Minoux M. Dioids and semirings: links to fuzzy sets and other applications[J]. Fuzzy Sets and Systems,2007,158:1273-1294.
[5]  Zimmermann U. Linear and combinatorial optimization in ordered algebraic structures[J]. Bull Am Math Soc,1985,12(1):148-149.
[6]  Luce R D. A note on Boolean matrix theory[J]. Proc Am Math Society,1952,3:382-388.
[7]  Rutherford D E. Inverses of Boolean matrices[J]. Proc Glasgow Math Association,1963,6:49-53.
[8]  Give’on Y. Matrix over semirings[J]. Info Control,1964,7:477-484.
[9]  Reutenauer C, Straubing Howard. Inversion of matrices over a commutative semiring[J]. J Algebra,1984,88:350-360.
[10]  Zhao C K. Inverses of L-fuzzy matrices[J]. Fuzzy Sets and Systems,1990,34:103-116.
[11]  Han S C, Li H X. Invertible incline matrices and Cramer’s rule over inclines[J]. Linear Algebra and Its Appl,2004,389:121-138.
[12]  Tan Y J. On invertible matrices over antirings[J]. Linear Algebra and Its Appl,2007,423:428-444.
[13]  Cechlacutearovacutea K, Placuteavka J. Linear independence in bottleneck algebras[J]. Fuzzy Sets and Systems,1996,77:337-348.
[14]  Cuninghame-Green R A, Butkovic P. Bases in max-algebra[J]. Linear Algebra and Its Appl,2004,389:107-120.
[15]  Gondran M, Minoux M. Graphs, Diods and Semirings[M]. New York:Springer-Verlag,2008.
[16]  Perfilieva I, Kupka J. Kronecker-Capelli theorem in semilinear spaces[C]//Proceedings of the 9th International FLINS Conference. Ruan D, Li T R, Xu Y, et al. New York:World Scientific,2010:43-51.
[17]  Brouwer R K. A method of relational fuzzy clustering based on producing feature vectors using fast map[J]. Info Sci,2009,179:3561-3582.
[18]  Cao Z Q, Kim K H, Roush F W. Incline Algebra and Applications[M]. New York:Ellis Horwood Ltd,1984.
[19]  Ghazinoory S, Esmail Zadeh A, Kheirkhah A S. Application of fuzzy calculations for improving portfolio matrices[J]. Info Sci,2010,180:1582-1590.
[20]  Give’on Y. Lattice matrices[J]. Info Control,1964,7:477-484.
[21]  Gondran M, Minoux M. Graphs Diods and Semirings[M]. New York:Springer-Verlag,2008.
[22]  Kim K H, Roush F W. Generalized fuzzy matrices[J]. Fuzzy Sets and Systems,1980,4:293-315.
[23]  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,2010,180:3232-3247.
[24]  Xu Z. A method based on distance measure for interval-valued intuitionistic fuzzy group decision making[J]. Info Sci,2010,180:181-190.
[25]  Zhao X Z, Jun Y B, Ren F. The semiring of matrices over a finite chain[J]. Inform Sci,2008,178:3443-3450.
[26]  Baccelli F L, Mairesse I. Ergodic theorems for stochastic operators and discrete event networks[C]//J Gunawardena. Bristol:Publ Newton Inst. Cambridge:Cambridge University Press,1998:171-208.

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