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Total Positivity: A New Inequality and Related Classes of Matrices

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Trends in Differential Equations and Applications

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 8))

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Abstract

In this paper we present the extension of some results to classes of matrices related to total positivity. First, we survey some properties and results for matrices with Signed Bidiagonal Decomposition (SBD matrices), a class of matrices that contains Totally Positive (TP) matrices and their inverses. We also extend the affirmative answer of an inequality conjectured for the Frobenius norm of the inverse of matrices whose entries belong to [0, 1] to the class of nonsingular totally positive matrices.

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Acknowledgements

This work has been partially supported by the Spanish Research Grant MTM2015-65433, by Gobierno the Aragón and Fondo Social Europeo.

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Authors and Affiliations

  1. Centro Universitario de la Defensa/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    A. Barreras

  2. Dep. Applied Mathematics/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    J. M. Peña

Authors
  1. A. Barreras
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  2. J. M. Peña
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Correspondence to A. Barreras .

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Editors and Affiliations

  1. Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cadiz, Spain

    Francisco Ortegón Gallego

  2. Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cadiz, Spain

    María Victoria Redondo Neble

  3. Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cadiz, Spain

    José Rafael Rodríguez Galván

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Barreras, A., Peña, J.M. (2016). Total Positivity: A New Inequality and Related Classes of Matrices. In: Ortegón Gallego, F., Redondo Neble, M., Rodríguez Galván, J. (eds) Trends in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-32013-7_21

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