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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 Matematica (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 Stevanovic
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 Angeles Carmona,
focuses on boundary value problems on finite networks with special
in-depth on the M-matrix inverse problem.
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