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- W2951587701 abstract "The Hermite Normal Form (HNF) is a canonical representation of matrices over any principal ideal domain. Over the integers, the distribution of the HNFs of randomly looking matrices is far from uniform. The aim of this article is to present an explicit computation of this distribution together with some applications. More precisely, for integer matrices whose entries are upper bounded in absolute value by a large bound, we compute the asymptotic number of such matrices whose HNF has a prescribed diagonal structure. We apply these results to the analysis of some procedures and algorithms whose dynamics depend on the HNF of randomly looking integer matrices." @default.
- W2951587701 created "2019-06-27" @default.
- W2951587701 creator A5028915374 @default.
- W2951587701 date "2010-09-24" @default.
- W2951587701 modified "2023-09-27" @default.
- W2951587701 title "Natural Density Distribution of Hermite Normal Forms of Integer Matrices" @default.
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