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Surjectivity of near-square random matrices

Part of: Special matrices Linear algebraic groups and related topics

Published online by Cambridge University Press:  06 November 2019

Hoi. H. Nguyen  and
Elliot Paquette
Hoi. H. Nguyen*
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH43210, USA
Elliot Paquette
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH43210, USA
*
*Corresponding author. Email: nguyen.1261@math.osu.edu
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Abstract

We show that a nearly square independent and identically distributed random integral matrix is surjective over the integral lattice with very high probability. This answers a question by Koplewitz [6]. Our result extends to sparse matrices as well as to matrices of dependent entries.

MSC classification

Primary: 15B52: Random matrices
Secondary: 20G40: Linear algebraic groups over finite fields
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 2 , March 2020 , pp. 267 - 292
Copyright
© Cambridge University Press 2019

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Footnotes

†

The first author is supported by research grants DMS-1600782 and DMS-1752345.

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