Determinant: Old Algorithms, New Insights

Mahajan, Meena ; Vinay, V. (1999) Determinant: Old Algorithms, New Insights SIAM Journal on Discrete Mathematics, 12 (4). pp. 474-490. ISSN 0895-4801

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n 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.

Item Type:Article
Source:Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords:determinant; Algorithms; Combinatorics; Graphs; Matrices
ID Code:127981
Deposited On:14 Oct 2022 11:32
Last Modified:14 Oct 2022 11:32

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