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Global product structure for a space of special matrices

  • Baltazar Aguirre-Hernández
  • Francisco A. Carrillo
  • Jesús F. EspinozaEmail author
  • Horacio Leyva
Original Article

Abstract

The importance of the Hurwitz–Metzler matrices and the Hurwitz symmetric matrices can be appreciated in different applications: communication networks, biology and economics are some of them. In this paper, we use an approach of differential topology for studying such matrices. Our results are as follows: the space of the \(n\times n\) Hurwitz symmetric matrices has a product manifold structure given by the space of the \((n-1)\times (n-1)\) Hurwitz symmetric matrices and the Euclidean space. Additionally we study the space of Hurwitz–Metzler matrices and these ideas let us do an analysis of robustness of Hurwitz–Metzler matrices. In particular, we study the insulin model as an application.

Keywords

Hurwitz–Metzler matrices Hurwitz symmetric matrices Insulin model Product manifold 

Mathematics Subject Classification

15B99 93D09 (primary) 57R55 (secondary) 

Notes

Acknowledgements

Jesús F. Espinoza acknowledges the financial support of CONACyT and of the Universidad de Sonora.

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Copyright information

© Sociedad Matemática Mexicana 2017

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversidad de SonoraHermosilloMexico
  2. 2.Mathematics DepartmentUniversidad Autónoma Metropolitana-IztapalapaMexico CityMexico

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