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.
- ISBN13 9781107095458
- Publish Date 12 February 2018 (first published 9 February 2018)
- Publish Status Active
- Out of Print 6 June 2022
- Publish Country GB
- Imprint Cambridge University Press
- Format Hardcover
- Pages 310
- Language English