- Publisher: Cambridge University Press
- Expected online publication date: January 2018
- Print publication year: 2018
- Online ISBN: 9781316155158
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.
Shaun M. Fallat - University of Regina, Canada
Beresford Parlett - University of California, Berkeley
Bryan Shader - University of Wyoming.