The determinant of random power series matrices over finite fields
type: Item
instance of: scholarly article
title: The determinant of random power series matrices over finite fields
zbMATH Open document ID: 0964.15016
DOI: 10.1016/S0024-3795(00)00134-8
author: Khaled Abdel-Ghaffar
published in: Linear Algebra and its Applications
publication date: 2001-07-19T00:00:00Z
review text: The set \(M_{n\times n}(F_qx)\) of \(n\times n\)-matrices \(A\) with elements \(a_{ij}= \sum a_{ijt} x^t\in\mathbb F_qx\) \((t\geq 0)\) is considered where \(\mathbb F_qx\) denotes the ring of formal power series over the finite field \(\mathbb F_q\) of \(q\) elements. The probability distribution is studied of the coefficient \(d_t\) of the determinant \(\det(A)= \sum d_tx^t\) \((t\geq 0)\) if \(A\) is random, i.e. if the coefficients of the entries of \(A\) are statistically independent and uniform over the elements of the finite field \(\mathbb F_q\).
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 1523266
zbMATH Keywords: random power series
zbMATH Keywords: matrices
zbMATH Keywords: determinants
zbMATH Keywords: finite fields
zbMATH Keywords: probability distribution
reviewed by: A. A. Bogush
MaRDI profile type: Publication
cites work: Q4146776
cites work: Determinants and ranks of random matrices over \({\mathbb{Z}}_ m\)
cites work: Subspaces, subsets, and partitions
Recommended article: On finite determinacy for matrices of power series
Recommended article: Some new results in random matrices over finite fields
Recommended article: Random matrix theory over finite fields
Recommended article: On the probability that the determinant of an n\(\times n\) matrix over a finite field vanishes
Recommended article: Distribution of determinant of matrices with restricted entries over finite fields
Recommended article: Remarks on the probability the determinant of an n\(\times n\)-matrix over a finite field vanishes
Recommended article: Q5576597
Recommended article: Powers of large random unitary matrices and Toeplitz determinants
Recommended article: Determinants and ranks of random matrices over \({\mathbb{Z}}_ m\)
Recommended article: Singularity probabilities for random matrices over finite fields
description: scientific article; zbMATH DE number 1523266