Natural Density of Rectangular Unimodular Integer Matrices

Details Natural Density of Rectangular Unimodular Integer Matrices Natural Density of Rectangular Unimodular Integer Matrices

2010-05-21

arxiv.org/abs/1005.3967v2

Mathematics

Number Theory

8 pages

Scientific paper

In this paper, we compute the natural density of the set of k x n integer
matrices that can be extended to an invertible n x n matrix over the integers.
As a corollary, we find the density of rectangular matrices with Hermite normal
form [O Id]. Connections with Cesaro's Theorem on the density of coprime
integers and Quillen-Suslin's Theorem are also presented.

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