Combinatorial Matrix Theory

  • Richard A. Brualdi
  • Ángeles Carmona
  • P. van den Driessche
  • Stephen Kirkland
  • Dragan Stevanović
  • Andrés M. Encinas
  • Margarida Mitjana

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Richard A. Brualdi
    Pages 1-46
  3. P. van den Driessche
    Pages 47-82
  4. Dragan Stevanović
    Pages 83-130
  5. Ángeles Carmona
    Pages 173-217
  6. Back Matter
    Pages 219-219

About this book

Introduction

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Keywords

permutation matrices tournament matrices sign pattern matrices generalized inverses adjacency laplacian eigenvalues and eigenvectors discrete potential theory

Authors and affiliations

  • Richard A. Brualdi
    • 1
  • Ángeles Carmona
    • 2
  • P. van den Driessche
    • 3
  • Stephen Kirkland
    • 4
  • Dragan Stevanović
    • 5
  1. 1.Mathematics DepartmentUniversity of Wisconsin Mathematics DepartmentMadisonUSA
  2. 2.Departament de MatemàtiquesUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  4. 4.Department of MathematicsUniversity of ManitobaWinnipegCanada
  5. 5.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia

Editors and affiliations

  • Andrés M. Encinas
    • 1
  • Margarida Mitjana
    • 2
  1. 1.Departament de MatemàtiquesEscola d'Enginyeria de Barcelona Est Departament de MatemàtiquesBarcelonaSpain
  2. 2.Departament de MatemàtiquesEscola d'Enginyeria de Barcelona Est Departament de MatemàtiquesBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-70953-6
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-70952-9
  • Online ISBN 978-3-319-70953-6
  • Series Print ISSN 2297-0304
  • Series Online ISSN 2297-0312
  • About this book