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Natural density of rectangular unimodular integer matrices


Maze, G; Rosenthal, J; Wagner, U (2011). Natural density of rectangular unimodular integer matrices. Linear Algebra and its Applications, 434(5):1319-1324.

Abstract

An integer matrix of size k×n, k≤n, is called unimodular if it can be extended to an n×n invertible matrix. The natural density of unimodular k×n matrices, which may be explained as the “probability" of a random k×n integer matrix to be unimodular, is determined in this paper using the Riemann's zeta function. The present result is a generalization of a classical result due to Cesáro and is also related to Quillen-Suslin's Theorem .

Abstract

An integer matrix of size k×n, k≤n, is called unimodular if it can be extended to an n×n invertible matrix. The natural density of unimodular k×n matrices, which may be explained as the “probability" of a random k×n integer matrix to be unimodular, is determined in this paper using the Riemann's zeta function. The present result is a generalization of a classical result due to Cesáro and is also related to Quillen-Suslin's Theorem .

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:09 Jan 2012 16:22
Last Modified:05 Apr 2016 15:17
Publisher:Elsevier
ISSN:0024-3795
Publisher DOI:https://doi.org/10.1016/j.laa.2010.11.015
Related URLs:http://arxiv.org/abs/1005.3967

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Content: Accepted Version
Filetype: PDF (Version 2)
Size: 124kB