# A simple division−free algorithm for computing determinants

*Richard S. Bird*

### 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 n×n matrix, where M(n) is the number of such operations needed for matrix multiplication. A direct combinatorial proof of correctness is given.

Journal

Information Processing Letters

Year

2011