Bounds for sums of eigenvalues and applications
Abstract
Let A be a matrix of order n x n with real spectrum lambda(1) greater than or equal to lambda(2) greater than or equal to ... greater than or equal to lambda(n). Let 1 less than or equal to k less than or equal to n - 2. If lambda(n) or lambda(1) is known, then we find an upper bound (respectively, lower bound) for the sum of the k-largest (respectively, k-smallest) remaining eigenvalues of A. Then, we obtain a majorization vector for (lambda(1),lambda(2),...,lambda(n-1)) when lambda(n) is known and a majorization vector for (lambda(2), lambda(3), ... ,lambda(n)) when lambda(1) is known. We apply these results to the eigenvalues of the Laplacian matrix of a graph and, in particular, a sufficient condition for a graph to be connected is given. Also, we derive an upper bound for the coefficient of ergodicity of a nonnegative matrix with real spectrum. (C) 2000 Elsevier Science Ltd. All rights reserved.
Más información
Título según WOS: | Bounds for sums of eigenvalues and applications |
Título según SCOPUS: | Bounds for sums of eigenvalues and applications |
Título de la Revista: | COMPUTERS & MATHEMATICS WITH APPLICATIONS |
Volumen: | 39 |
Número: | 7-8 |
Editorial: | PERGAMON-ELSEVIER SCIENCE LTD |
Fecha de publicación: | 2000 |
Página de inicio: | 1 |
Página final: | 15 |
Idioma: | English |
URL: | http://linkinghub.elsevier.com/retrieve/pii/S0898122100000602 |
DOI: |
10.1016/S0898-1221(00)00060-2 |
Notas: | ISI, SCOPUS |