Natural Density of Rectangular Unimodular Integer Matrices
Number Theory
2010-11-23 v2 Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.1005.3967,
title = {Natural Density of Rectangular Unimodular Integer Matrices},
author = {G. Maze and J. Rosenthal and U. Wagner},
journal= {arXiv preprint arXiv:1005.3967},
year = {2010}
}
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8 pages