Combinatorial and Graph-Theoretical Problems in Linear Algebra

Brualdi Richard A. Klee Victor Friedland Shmuel

ISBN 10: 1461383560 / ISBN 13: 9781461383567

Editore: Springer, 2011

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Codice articolo 1854514558

Dati bibliografici

• Titolo: Combinatorial and Graph-Theoretical Problems in Linear Algebra
• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 1461383560
• ISBN 13: 9781461383567
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

This book presents past and current research on combinatorial and graph-theoretical problems in linear algebra. It offers a glimpse of the increasing role of combinatorial structure in matrix analysis and conversely, of the powerful tool that linear algebra provides in combinatorics and graph theory. The material covered will be of interest to researchers in linear algebra, combinatorics and graph theory.

Contenuti

Symbolic dynamics and matrices.- Mixed matrices: Irreducibility and decomposition.- A geometric approach to the Laplacian matrix of a graph.- Qualitative semipositivity.- Eigenvalues in combinatorial optimization.- Eutactic stars and graph spectra.- Some matrix patterns arising in queuing theory.- Laplacian unimodular equivalence of graphs.- Rank incrementation via diagonal perturbations.- Eigenvalues of almost skew symmetric matrices and tournament matrices.- Combinatorial orthogonality.- The symmetric group as a polynomial space.- Completely positive graphs.- Hadamard matrices.- Self-inverse sign patterns.- Open problems.