A simple division-free algorithm for computing determinants

Authors:
Richard S. Bird
Affiliations:
Department of Computer Science, Oxford University, Wolfson Building, Parks Rd, Oxford, OX1 3QD, UK
Venue:
Information Processing Letters
Year:
2011

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Abstract

We present an extremely simple method for computing determinants, one that uses no division operations, exact or otherwise. The method amounts to no more than iterating a certain matrix multiplication and requires O(nM(n)) additions and multiplications for an nxn matrix, where M(n) is the number of such operations needed for matrix multiplication. A direct combinatorial proof of correctness is given.