Fecha
2021-03-05
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info:eu-repo/semantics/openAccess
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International Linear Algebra Society (ILAS)
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Resumen
In recent years, there has been a growing interest in companion matrices. Sparse companion matrices are well known: every sparse companion matrix is equivalent to a Hessenberg matrix of a particular simple type. Recently, Deaett et al. [Electron. J. Linear Algebra, 35:223247, 2019] started the systematic study of nonsparse companion matrices. They proved that every nonsparse companion matrix is nonderogatory, although not necessarily equivalent to a Hessenberg matrix. In this paper, the nonsparse companion matrices which are unit Hessenberg are described. In a companion matrix, the variables are the coordinates of the characteristic polynomial with respect to the monomial basis. A PB-companion matrix is a generalization, in the sense that the variables are the coordinates of the characteristic polynomial with respect to a general polynomial basis. The literature provides examples with Newton basis, Chebyshev basis, and other general orthogonal bases. Here, the PB-companion matrices which are unit Hessenberg are also described.
Descripción
The registered version of this article, first published in Electronic Journal of Linear Algebra, is available online at the publisher's website: International Linear Algebra Society (ILAS), https://doi.org/10.13001/ela.2021.5405
La versión registrada de este artículo, publicado por primera vez en Electronic Journal of Linear Algebra, está disponible en línea en el sitio web del editor: International Linear Algebra Society (ILAS), https://doi.org/10.13001/ela.2021.5405
La versión registrada de este artículo, publicado por primera vez en Electronic Journal of Linear Algebra, está disponible en línea en el sitio web del editor: International Linear Algebra Society (ILAS), https://doi.org/10.13001/ela.2021.5405
Categorías UNESCO
Palabras clave
Companion matrix, Characteristic polynomial, Hessenberg matrix, Polynomial basis, Nilpotent matrix
Citación
Borobia, A., & Canogar, R. (2021). Nonsparse companion hessenberg matrices. Electronic Journal of Linear Algebra, 37, 193-210. https://doi.org/10.13001/ELA.2021.5405
Centro
Facultad de Ciencias
Departamento
Matemáticas Fundamentales