Natural density of rectangular unimodular integer matrices

DOI10.1016/j.laa.2010.11.015zbMath1211.15044arXiv1005.3967OpenAlexW2137127771MaRDI QIDQ624535

Gérard Maze, Joachim Rosenthal, Urs Wagner

Publication date: 9 February 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3967

zbMATH Keywords

natural densityunimodular matrixCesáro's TheoremQuillen-Suslin's Theorem

Mathematics Subject Classification ID

Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (13)

The corank of a rectangular random integer matrix ⋮ Counting basis extensions in a lattice ⋮ Random systems of equations in free abelian groups. ⋮ Uniform probability and natural density of mutually left coprime polynomial matrices over finite fields ⋮ The probability of rectangular unimodular matrices over \(\mathbb F_q[x\)] ⋮ Loop-abort faults on lattice-based Fiat-Shamir and hash-and-sign signatures ⋮ On the probability of generating a lattice ⋮ Natural density distribution of Hermite normal forms of integer matrices ⋮ Representing integers by multilinear polynomials ⋮ On Rectangular Unimodular Matrices over the Algebraic Integers ⋮ Natural density of integral matrices that can be extended to invertible integral matrices ⋮ ON THE MERTENS–CESÀRO THEOREM FOR NUMBER FIELDS ⋮ Unimodular polynomial matrices over finite fields

Cites Work

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• Completion of a partial integral matrix to a unimodular matrix
• On the completion of a partial integral matrix to a unimodular matrix
• On the probability that \(k\) positive integers are relatively prime. II
• The Quillen - Suslin theorem and the structure of n-dimensional elementary polynomial matrices
• The Probability that a Matrix of Integers Is Diagonalizable
• Projective modules over polynomial rings

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