Some asymptotics for triangular matrices over finite fields
type: Item
instance of: scholarly article
title: Some asymptotics for triangular matrices over finite fields
zbMATH Open document ID: 0940.15018
DOI: 10.1016/S0024-3795(98)10067-8
author: Frank III Gerth
published in: Linear Algebra and its Applications
publication date: 2000-07-17T00:00:00Z
review text: The author compares the asymptotic behavior of certain probabilities for upper triangular matrices over the finite field \(F_{q}\) to the asymptotic behavior of the corresponding probabilities for arbitrary matrices. As \(q\rightarrow \infty \), the probability that an \(n\times n\) upper triangular matrix over \(F_{q}\) has rank equal to \(n\) (or being the matrix diagonalizable) approaches \(1\). Similar results are obtained for arbitrary matrices.
reviewed by: M. Ladra
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 1370167
zbMATH Keywords: triangular matrices
zbMATH Keywords: probability
zbMATH Keywords: rank
zbMATH Keywords: corank
zbMATH Keywords: diagonalizable matrices
zbMATH Keywords: finite field
zbMATH Keywords: asymptotic behavior
MaRDI profile type: Publication
cites work: Limit probabilities for coranks of matrices over GF(q)
cites work: Some probabilities for eigenvalues of matrices with entries in finite fields
cites work: Some asymptotic results on finite vector spaces
description: scientific article; zbMATH DE number 1370167