Determinant: Old Algorithms, New Insights

Authors:
Meena Mahajan;V. Vinay
Affiliations:
-;-
Venue:
SIAM Journal on Discrete Mathematics
Year:
1999

Citing 0
Cited 6

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The quantum query complexity of the determinant

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Noncommutativity makes determinants hard

ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I

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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 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.