© 2018

Combinatorial Matrix Theory

  • Andrés M. Encinas
  • Margarida Mitjana
  • Focuses on permutation, alternating sign and tournament matrices

  • Includes an introduction to boundary value problems and related techniques on finite networks

  • Discusses applications of the group inverse of the Laplacian matrix


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


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.


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

Authors and affiliations

  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

About the editors

Richard A. Brualdi is an Emeritus Professor at the University of Wisconsin in Madison, WI, USA.

Pauline van den Driessche is an Emeritus Professor at the University of Victoria, Canada.

Dragan Stevanović is a Full Research Professor at the Serbian Academy of Sciences and Arts in Belgrade, Serbia.

Stephen Kirkland is a Professor at the University of Manitoba in Winnipeg, Canada.

Ángeles Carmona is an Associate Professor at the Universitat Politècnica de Catalunya in Barcelona, Spain. 

Bibliographic information


“A very excellent treatment of the subject for mathematicians interested in the intersection between matrix theory and combinatorics. … it is appropriate for graduate students and others interested in the latest developments in this rich and diverse field.” (MAA Reviews, March 1, 2020)