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Combinatorial Matrix Theory

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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.

Authors: Brualdi Richard, Carmona Angeles, van den Driessche P., Kirkland Stephen, Stevanovic Dragan, Encinas Andres, Mitjana Margarida
Pages: 219
ISBN: 9783319709529
Cover: Paperback
Edition Number: 1
Release Year: 2018

Some combinatorially defined matrix class.- Sign pattern matrices.- The spectral radius of a graph.- The group inverse of the Laplacian matrix of a graph.- Boundary value problems on finite networks.

Richard A. Brualdi, University of Wisconsin Mathematics Department, Madison, WI, USA

Ángeles Carmona, Universitat Politècnica de Catalunya, Barcelona, Spain

P. van den Driessche, University of Victoria, Victoria, BC, Canada

Stephen Kirkland, University of Manitoba, Winnipeg, MB, Canada

Dragan Stevanović, Serbian Academy of Sciences and Arts, Belgrade, Serbia

 Andrés M. Encinas, Escola d'Enginyeria de Barcelona Est Departament de Matemàtiques, Barcelona, Spain

 Margarida Mitjana, Escola d'Enginyeria de Barcelona Est Departament de Matemàtiques, Barcelona, Spain

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