Bézoutians of rational matrix functions, matrix equations and factorizations
type: Item
instance of: scholarly article
title: Bézoutians of rational matrix functions, matrix equations and factorizations
zbMATH Open document ID: 0958.15007
DOI: 10.1016/S0024-3795(99)00068-3
author: Leonid Lerer
author: Leiba Rodman
published in: Linear Algebra and its Applications
publication date: 2002-03-19T00:00:00Z
review text: Interconnections between Bézoutians of rational matrix functions, linear and quadratic equations and factorizations of rational matrix functions are studied. The Bézoutians are characterized as the angle operators generated by certain pairs of invariant subspaces. The factorizations \(F_I(\lambda)F(\lambda)= G_I(\lambda)G(\lambda)\), where \(F_I(\lambda)\), \(F(\lambda)\), \(G_I(\lambda)\), \(G(\lambda)\) are \(n\times n\) rational matrix functions, are described via the Bézoutian angle operators. Coprime factorizations and invertible solutions of Sylvester equations, different types of factorizations and doubly coprime minimal factorizations are discussed.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 93B28
zbMATH DE Number: 1419862
zbMATH Keywords: matrix equations
zbMATH Keywords: operator methods
zbMATH Keywords: realization
zbMATH Keywords: Bézoutians
zbMATH Keywords: rational matrix functions
zbMATH Keywords: factorizations
zbMATH Keywords: invariant subspaces
zbMATH Keywords: Sylvester equations
zbMATH Keywords: doubly coprime minimal factorizations
Wikidata QID: Q114122536
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1419862