Methods for constructing distance matrices and the inverse eigenvalue problem
type: Item
instance of: scholarly article
title: Methods for constructing distance matrices and the inverse eigenvalue problem
zbMATH Open document ID: 0935.15004
DOI: 10.1016/S0024-3795(99)00065-8
published in: Linear Algebra and its Applications
publication date: 1999-11-29T00:00:00Z
review text: Necessary conditions are provided on \(Z\) in order that \(D=\left[ \begin{smallmatrix} D_1 & Z\\ Z^T & D_2\end{smallmatrix}\right]\in\mathbb{R}^{n\times n}\) is a distance matrix \((D_1,D_2\) are distance matrices). To construct an \((n+1) \times (n+1)\) distance matrix it is always possible to border an \(n\times n\) distance matrix with certain scalar multiples of the Perron eigenvector. Necessary and sufficient conditions are obtained for the use of the Perron eigenvector related to the \(D_1\) and \(D_2\) blocks in the formation of the above distance matrix. The solution of the inverse eigenvalue problem is discussed. The case of the existence of a Hadamard matrix is included.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1371416
zbMATH Keywords: distance matrix
zbMATH Keywords: Perron eigenvector
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: Hadamard matrix
author: Thomas L. Hayden
author: Robert Reams
author: James H. Wells
MaRDI profile type: Publication
Wikidata QID: Q127109511
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description: scientific article; zbMATH DE number 1371416