Determinant: Old Algorithms, New Insights

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. Key words. determinant, algorithms, combinatorics, graphs, matrices AMS subject classifications. 05A15, 68R05, 05C50, 68Q25 PII. S0895480198338827

• Type: Journal
• Year: 1998
• Where: ECCC
• Authors: Meena Mahajan, V. Vinay
• Keywords: Characteristic Polynomial, Combinatorial Characterizations, Combinatorial Viewpoint, ECCC 1998