On matrices with common invariant cones with applications in neural and gene networks
type: Item
instance of: scholarly article
title: On matrices with common invariant cones with applications in neural and gene networks
zbMATH Open document ID: 1070.15017
author: R. Edwards
author: M. Tsatsomeros
author: J. J. McDonald
published in: Linear Algebra and its Applications
publication date: 2005-05-04T00:00:00Z
review text: The authors describe and investigate matrix theoretic problems that arise in the study of the dynamic of Glass networks. Glass networks are described in detail in Section 2. Sections 3 and 4 contain notation, definition and preliminary observations regarding invariant set and cones. In Section 5 they consider the topological properties of the set of all words of finite length constructed from two matrices. In Section 6, they consider the case of commuting matrices. The problem of common invariant proper cones is examined for \(2\times 2\) matrices in Section 7. The case of common invariant polyhedral cones is analyzed and recast in a multilinear framework in Section 8.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 15A75
zbMATH DE Number: 2165372
zbMATH Keywords: invariant cone
zbMATH Keywords: proper cone
zbMATH Keywords: invariant subspace
zbMATH Keywords: matrix word
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: Perron-Frobenius
zbMATH Keywords: tensor product
zbMATH Keywords: compound matrix
zbMATH Keywords: exterior product
zbMATH Keywords: decomposable vector
zbMATH Keywords: dominant eigenvector
zbMATH Keywords: Glass network
zbMATH Keywords: gene network
zbMATH Keywords: neural network
zbMATH Keywords: Cantor set
MaRDI profile type: Publication
full work available at URL: j.laa.2004.04.005
OpenAlex ID: W2161993753
Wikidata QID: Q57942489
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DOI: 10.1016/J.LAA.2004.04.005
description: scientific article; zbMATH DE number 2165372