Eigenspace of a circulant max–min matrix

Martin Gavalec; Hana Tomášková

Kybernetika (2010)

  • Volume: 46, Issue: 3, page 397-404
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Gavalec, Martin, and Tomášková, Hana. "Eigenspace of a circulant max–min matrix." Kybernetika 46.3 (2010): 397-404. <http://eudml.org/doc/197177>.

@article{Gavalec2010,
abstract = {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.},
author = {Gavalec, Martin, Tomášková, Hana},
journal = {Kybernetika},
keywords = {(max; min) algebra; eigenvector; circulant matrix; max-min algebra; circulant matrix; eigenvector},
language = {eng},
number = {3},
pages = {397-404},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Eigenspace of a circulant max–min matrix},
url = {http://eudml.org/doc/197177},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Gavalec, Martin
AU - Tomášková, Hana
TI - Eigenspace of a circulant max–min matrix
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 397
EP - 404
AB - 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.
LA - eng
KW - (max; min) algebra; eigenvector; circulant matrix; max-min algebra; circulant matrix; eigenvector
UR - http://eudml.org/doc/197177
ER -

References

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  2. Cuninghame-Green, R. A., Minimax Algebra, (Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin, 1979. Zbl0739.90073MR0580321
  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. 
  4. Gavalec, M., 10.1016/S0024-3795(01)00488-8, Lin. Algebra Appl. 345 (2002), 149–167. Zbl0994.15010MR1883271DOI10.1016/S0024-3795(01)00488-8
  5. Gavalec, M., Plavka, J., Eigenproblem in extremal algebras, In: Proc. 9th Internat. Symposium Operations Research ’07, Nova Gorica, Slovenia 2007. Zbl1135.15004
  6. Gray, R. M., Toeplitz and Circulant Matrices, Now Publishers, Delft 2006. Zbl1115.15021
  7. Plavka, J., 10.1080/02331930108844576, Optimization 50 (2001), 477–483. Zbl1005.90054MR1892917DOI10.1080/02331930108844576
  8. Plavka, J., 10.1016/j.dam.2005.02.017, Discrete Applied Mathematics 150 (2005), 16–28. MR2161336DOI10.1016/j.dam.2005.02.017
  9. Zimmermann, K., Extremal Algebra (in Czech), Ekon. ústav ČSAV, Praha 1976. 
  10. Zimmermann, U., Linear and Combinatorial Optimization in Ordered Algebraic Structure, (Ann. Discrete Math. 10.) North Holland, Amsterdam 1981. MR0609751

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