The maximum determinant of 21\(\times 21\) \((+1,-1)\)-matrices and D-optimal designs
type: Item
instance of: scholarly article
title: The maximum determinant of 21\(\times 21\) \((+1,-1)\)-matrices and D-optimal designs
zbMATH Open document ID: 0625.62062
DOI: 10.1016/0378-3758(87)90066-8
author: Theo Chadjipantelis
author: Stratis Kounias
author: Chronis Moyssiadis
published in: Journal of Statistical Planning and Inference
publication date: 1987-01-01T00:00:00Z
review text: In this paper the authors give a square matrix \(R^*\) of size 21 with elements -1, \(+1\) such that det \(M^*=\det (R^{*T}R^*)=20^{18}(116)^ 2\), and that \(R^*\) is the D-optimal design, i.e. the matrix \(R^*\) has the maximum determinant. In order to prove this D-optimality, a computational procedure is given to obtain all (21\(\times 21)\) symmetric and positive-definite matrices \(M=(m_{ij})\), \(m_{ii}=21\), \(m_{ij}\equiv 1(mod 4)\), \(i\neq j\), such that det (M)\(=square\) of an integer and det \(M\geq 20^{18}(116)^ 2\). It is shown that, besides \(M^*\), there are two more such matrixes \(M_ 1\), \(M_ 2\) which are shown not to exist.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 62K10
zbMATH DE Number: 4015962
zbMATH Keywords: maximum determinant
zbMATH Keywords: D-optimality
MaRDI profile type: Publication
full work available at URL: 0378-3758(87)90066-8
OpenAlex ID: W1979693101
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description: scientific article; zbMATH DE number 4015962