Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772937 | Linear Algebra and its Applications | 2018 | 16 Pages |
Abstract
For real symmetric, or complex Hermitian, matrices whose graph is a tree, there is a well-developed (via several papers) theory about the possible multiplicities of the eigenvalues. It includes a theory of vertices whose removal increases a multiplicity (the “Parter-Wiener, etc. theory” and the “downer branch mechanism”), how to determine maximum multiplicity, lower bounds for the minimum number of distinct eigenvalues, etc. Remarkably, a great deal of this theory may be generalized to geometric multiplicities of general matrices over a field (with very different proofs). We show here what parts of this theory generalize, and, in the process, review the theory.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Charles R. Johnson, Carlos M. Saiago,