The probability of rectangular unimodular matrices over Fq[x]

被引：8
|
作者：
Guo, Xiangqian [1 ]
Yang, Guangyu [1 ]
机构：
[1] Zhengzhou Univ, Dept Math, Zhengzhou 450001, Henan Province, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 06期
关键词：
Natural density; Unimodular matrices; Riemann's zeta function; q-Zeta function; Finite field; Polynomial ring;
D O I：
10.1016/j.laa.2012.11.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note, we show that the probability that a uniformly random k x n matrix over F-q[x] can be extended to an n x n invertible matrix is (1 - q(k-n)) (1 - q(k-1-n)) ... (1-q(1-n)). Connections with Dirichlet's density theorem on co-prime integers and its various generalizations are also presented. (C) 2012 Elsevier Inc. All rights reserved.
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页码：2675 / 2682
页数：8
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