Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8966124 | Linear Algebra and its Applications | 2018 | 17 Pages |
Abstract
It is known that an n-by-n Hermitian matrix, nâ¥2, whose graph is a tree necessarily has at least two eigenvalues (the largest and smallest, in particular) with multiplicity 1. Recently, much of the multiplicity theory, for eigenvalues of Hermitian matrices whose graph is a tree, has been generalized to geometric multiplicities of eigenvalues of matrices over a general field (whose graph is a tree). However, the two 1's fact does not generalize. Here, we give circumstances under which there are two 1's and give several examples (without two 1's) that limit our positive results.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Charles R. Johnson, António Leal-Duarte, Carlos M. Saiago,