Determinants of matrices of the conference type
type: Item
instance of: scholarly article
title: Determinants of matrices of the conference type
zbMATH Open document ID: 0878.15001
DOI: 10.1016/S0024-3795(96)00412-0
author: Brendan D. McKay
author: Jacob Seidel
author: Bussemaker, Frans C.
author: Irving Kaplansky
published in: Linear Algebra and its Applications
publication date: 1997-11-21T00:00:00Z
review text: An \(n\) by \(n\) conference type matrix has \(0\)'s on the main diagonal and \(\pm 1\)'s elsewhere. The authors investigate the largest possible determinant of such a matrix for \(n\) odd, \(n \leq 11.\) For \(n\) even, there is already an extensive literature but even there a few conjectures are still open. To get the matrices having largest determinant among conference matrices for \(n\) odd, \(n \leq 11,\) the authors use some intelligent techniques which help them in reducing their search drastically. The same techniques don't seem to work for higher values of \(n\). And even with their intelligent technique they had to use a huge CPU time. So, the problem seems to be very very difficult for large odd \(n\). At the end, I would like to add that their notation `P-matrix' (in honor of Paley) for certain matrices doesn't seem appropriate as this notation has already been accepted long back for certain class of matrices in the literature on Linear Complementarity Problem in Operations Research.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 1044260
zbMATH Keywords: determinant
zbMATH Keywords: conference matrix
zbMATH Keywords: symmetric positive definite matrix
zbMATH Keywords: Eulerian graphs
reviewed by: Arbind Kumar Lal
describes a project that uses: nauty
MaRDI profile type: Publication
cites work: The maximum determinant of 21\(\times 21\) \((+1,-1)\)-matrices and D-optimal designs
cites work: Orthogonal Matrices with Zero Diagonal. II
cites work: Determinantenabschätzungen für binäre Matrizen. (Estimation of determinants for binary matrices)
cites work: Q5723947
cites work: Orthogonal Matrices with Zero Diagonal
cites work: Matrix Analysis
cites work: Determinantal inequalities for positive definite matrices
cites work: Q5513521
cites work: Two-Graphs, Switching Classes and Euler Graphs are Equal in Number
cites work: The exact D-optimal first order saturated design with 17 observations
cites work: On Orthogonal Matrices
cites work: On Hadamard's inequality for the determinants of order non-divisible by 4
full work available at URL: s0024-3795(96)00412-0
OpenAlex ID: W2000737630
description: scientific article; zbMATH DE number 1044260