Eigenvalues, Multiplicities and Graphs (Hardcover)

Charles R. Johnson

ISBN 10: 110709545X / ISBN 13: 9781107095458

Published by Cambridge University Press, Cambridge, 2018

About this Item

Hardcover. The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. For mathematicians working with linear algebra, computation, and combinatorics, the book provides new information to extend the ideas to areas such as geometric multiplicities. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9781107095458

Bibliographic Details

• Title: Eigenvalues, Multiplicities and Graphs (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2018
• Language: English
• ISBN 10: 110709545X
• ISBN 13: 9781107095458
• Binding: Hardcover
• Condition: new

About this title

Synopsis

The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.

About the Authors

Charles R. Johnson is Class of 1961 Professor of Mathematics at the College of William and Mary, Virginia. He is the recognized expert in the interplay between linear algebra and combinatorics, as well as many parts of matrix analysis. He is coauthor of Matrix Analysis (Cambridge, 2012), Topics in Matrix Analysis (Cambridge, 2010), both with Roger Horn, and Totally Nonnegative Matrices (2011, with Shaun Fallat).

Carlos M. Saiago is Assistant Professor of Mathematics at Universidade Nova de Lisboa, Portugal, and is the author of fifteen papers on eigenvalues, multiplicities, and graphs.