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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 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 Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.
List of contents
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.
About the author
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.
Summary
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.
Additional text
“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)
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"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)
