How often do determinants over finite fields vanish?
type: Item
instance of: scholarly article
title: How often do determinants over finite fields vanish?
zbMATH Open document ID: 0623.15001
DOI: 10.1016/0012-365X(87)90217-2
author: William C. Waterhouse
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: \textit{A. Mukhopadhyay} [ibid. 51, 311-315 (1984; Zbl 0553.15003)] derived a formula for the probability that an \(n\times n\) matrix over a finite field has determinant zero. The author of the present note shows that the earlier formula is false and gives the correct result.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 4010683
zbMATH Keywords: singular matrix
zbMATH Keywords: finite field
zbMATH Keywords: determinant zero
reviewed by: George Phillip Barker
MaRDI profile type: Publication
cites work: Limit probabilities for coranks of matrices over GF(q)
cites work: Q3259107
cites work: On the probability that the determinant of an n\(\times n\) matrix over a finite field vanishes
full work available at URL: 0012-365x(87)90217-2
OpenAlex ID: W2030231691
description: scientific article; zbMATH DE number 4010683