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Title: Eigenspace of a circulant max–min matrix (English)
Author: Gavalec, Martin
Author: Tomášková, Hana
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 46
Issue: 3
Year: 2010
Pages: 397-404
Summary lang: English
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Category: math
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Summary: The eigenproblem of a circulant matrix in max-min algebra is investigated. Complete characterization of the eigenspace structure of a circulant matrix is given by describing all possible types of eigenvectors in detail. (English)
Keyword: (max, min) algebra
Keyword: eigenvector
Keyword: circulant matrix
MSC: 08A72
MSC: 15A18
MSC: 15A80
MSC: 90B35
MSC: 90C47
idZBL: Zbl 1206.15008
idMR: MR2676077
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Date available: 2010-09-13T16:48:35Z
Last updated: 2013-09-21
Stable URL: http://hdl.handle.net/10338.dmlcz/140755
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Reference: [1] Cechlárová, K.: Eigenvectors in bottleneck algebra.Lin. Algebra Appl. 175 (1992), 63–73. MR 1179341, 10.1016/0024-3795(92)90302-Q
Reference: [2] Cuninghame-Green, R. A.: Minimax Algebra.(Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin, 1979. Zbl 0739.90073, MR 0580321
Reference: [3] Cuninghame-Green, R. A.: Minimax Algebra and Application.In: Advances in Imaging and Electron Physics 90 (P. W. Hawkes, ed.), Academic Press, New York 1995.
Reference: [4] Gavalec, M.: Monotone eigenspace structure in max-min algebra.Lin. Algebra Appl. 345 (2002), 149–167. Zbl 0994.15010, MR 1883271, 10.1016/S0024-3795(01)00488-8
Reference: [5] Gavalec, M., Plavka, J.: Eigenproblem in extremal algebras.In: Proc. 9th Internat. Symposium Operations Research ’07, Nova Gorica, Slovenia 2007. Zbl 1135.15004
Reference: [6] Gray, R. M.: Toeplitz and Circulant Matrices.Now Publishers, Delft 2006. Zbl 1115.15021
Reference: [7] Plavka, J.: Eigenproblem for circulant matrices in max-algebra.Optimization 50 (2001), 477–483. Zbl 1005.90054, MR 1892917, 10.1080/02331930108844576
Reference: [8] Plavka, J.: l-parametric eigenproblem in max algebra.Discrete Applied Mathematics 150 (2005), 16–28. MR 2161336, 10.1016/j.dam.2005.02.017
Reference: [9] Zimmermann, K.: Extremal Algebra (in Czech).Ekon. ústav ČSAV, Praha 1976.
Reference: [10] Zimmermann, U.: Linear and Combinatorial Optimization in Ordered Algebraic Structure.(Ann. Discrete Math. 10.) North Holland, Amsterdam 1981. MR 0609751
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