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International Conference on Integer Programming and Combinatorial Optimization

IPCO 2005: Integer Programming and Combinatorial Optimization pp 335–348Cite as

Combinatorial Analysis of Generic Matrix Pencils

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3509))

Abstract

This paper investigates the Kronecker canonical form of matrix pencils under the genericity assumption that the set of nonzero entries is algebraically independent. We provide a combinatorial characterization of the sums of the row/column indices supported by efficient bipartite matching algorithms. We also give a simple alternative proof for a theorem of Poljak on the generic ranks of matrix powers.

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Author information

Authors and Affiliations

  1. University of Tokyo, Tokyo, 113-8656, Japan

    Satoru Iwata & Ryo Shimizu

Authors
  1. Satoru Iwata
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  2. Ryo Shimizu
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität zu Köln,  

    Michael Jünger

  2. Fakultät für Mathematik, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Volker Kaibel

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© 2005 Springer-Verlag Berlin Heidelberg

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Iwata, S., Shimizu, R. (2005). Combinatorial Analysis of Generic Matrix Pencils. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_25

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  • DOI: https://doi.org/10.1007/11496915_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26199-5

  • Online ISBN: 978-3-540-32102-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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