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arXiv · 1005.3967

Natural Density of Rectangular Unimodular Integer Matrices

G. Maze·J. Rosenthal·U. Wagner
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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.

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G. Maze, J. Rosenthal, U. Wagner. 2010-11-22. Natural Density of Rectangular Unimodular Integer Matrices. https://arxiv.org/abs/1005.3967

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