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Scandinavian Workshop on Algorithm Theory

SWAT 1998: Algorithm Theory — SWAT'98 pp 276–287Cite as

Determinant: Old algorithms, new insights

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1432))

Abstract

In this paper we approach the problem of computing the characteristic polynomial of a matrix from the combinatorial viewpoint. We present several combinatorial characterizations of the coefficients of the characteristic polynomial, in terms of walks and closed walks of different kinds in the underlying graph. We develop algorithms based on these characterizations, and show that they tally with well-known algorithms arrived at independently from considerations in linear algebra.

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Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, 600 113, Chennai, India

    Meena Mahajan

  2. Department of Computer Science and Automation, Indian Institute of Science, 560 012, Bangalore, India

    V. Vinay

Authors
  1. Meena Mahajan
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  2. V. Vinay
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Editor information

Stefan Arnborg Lars Ivansson

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© 1998 Springer-Verlag Berlin Heidelberg

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Mahajan, M., Vinay, V. (1998). Determinant: Old algorithms, new insights. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054375

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  • DOI: https://doi.org/10.1007/BFb0054375

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64682-2

  • Online ISBN: 978-3-540-69106-8

  • eBook Packages: Springer Book Archive

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