Title:
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Eigenspace of a circulant max–min matrix (English) |
Author:
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Gavalec, Martin |
Author:
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Tomášková, Hana |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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46 |
Issue:
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3 |
Year:
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2010 |
Pages:
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397-404 |
Summary lang:
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English |
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Category:
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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:
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(max, min) algebra |
Keyword:
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eigenvector |
Keyword:
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circulant matrix |
MSC:
|
08A72 |
MSC:
|
15A18 |
MSC:
|
15A80 |
MSC:
|
90B35 |
MSC:
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90C47 |
idZBL:
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Zbl 1206.15008 |
idMR:
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MR2676077 |
. |
Date available:
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2010-09-13T16:48:35Z |
Last updated:
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2013-09-21 |
Stable URL:
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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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