Determinant: Old algorithms, new insights

Extended abstract
  • Meena Mahajan
  • V. Vinay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1432)


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.


Characteristic Polynomial Tour Sequence Combinatorial Proof Combinatorial Interpretation Matrix Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Meena Mahajan
    • 1
  • V. Vinay
    • 2
  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

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