| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2010-09-13T16:48:35Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140755 |
| . |
| 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 |
| . |
