Combinatorial Matrix Theory

Richard A. Brualdi, Ángeles Carmona, P. van den Driessche, Stephen Kirkland, Dragan Stevanović (Autoren)

Andrés M. Encinas, Margarida Mitjana (Herausgeber)

Buch | Softcover

XI, 219 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-70952-9 (ISBN)

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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.

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 Stevanovic 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.

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.

"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)

Erscheinungsdatum	21.04.2018
Reihe/Serie	Advanced Courses in Mathematics - CRM Barcelona
Zusatzinfo	XI, 219 p.
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Gewicht	396 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	adjacency • combinatorics • discrete potential theory • Eigenvalues and Eigenvectors • generalized inverses • Laplacian • matrix theory • Ordinary differential equations • permutation matrices • sign pattern matrices • tournament matrices
ISBN-10	3-319-70952-6 / 3319709526
ISBN-13	978-3-319-70952-9 / 9783319709529
Zustand	Neuware