Determinant: old algorithms, new insights

Mahajan, Meena and Vinay, V (1999) Determinant: old algorithms, new insights. In: SIAM Journal on Discrete Mathematics, 12 (4). pp. 474-490.

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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 coeffcients 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.

Item Type:	Journal Article
Publication:	SIAM Journal on Discrete Mathematics
Publisher:	Society for Industrial and Applied Mathematics
Additional Information:	Copyright for this article belongs to Society for Industrial and Applied Mathematics (SIAM)
Keywords:	determinant;algorithms;combinatorics;graphs;matrices
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	02 Jun 2004
Last Modified:	19 Sep 2010 04:12
URI:	http://eprints.iisc.ac.in/id/eprint/65

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