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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Integral matrices of fixed rank


Author: Yonatan R. Katznelson
Journal: Proc. Amer. Math. Soc. 120 (1994), 667-675
MSC: Primary 11H06; Secondary 11P21
DOI: https://doi.org/10.1090/S0002-9939-1994-1169034-3
MathSciNet review: 1169034
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Abstract: Asymptotic formulæare derived for the number of $ n \times m$ matrices of fixed rank $ k$ with rational integral coefficients that are contained in a Euclidean ball of radius $ T$ in $ {{\mathbf{R}}^{n \times m}}$. It is assumed that $ n \geqslant m > k \geqslant 1$ are fixed, and the asymptotics are valid as $ T$ tends to infinity. The methods used are elementary.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1169034-3
Article copyright: © Copyright 1994 American Mathematical Society

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