Geodesic
A lower bound for the number of distinct eigenvalues of some real symmetric matrices
The electronic journal of linear algebra, Tome 21 (2010), pp. 3-11.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This mostly expository note surveys and recovers a lower bound for the number of distinct eigenvalues of real symmetric matrices associated with a graph. The relation is established with the length of some paths of the underlying graph, using an improvement of an inequality involving the multiplicities of the eigenvalues. An interesting use of that number is observed. Some applications of the results to particular classes of graphs are considered.
Classification : 05C50
Keywords: multiplicities, distinct eigenvalues, real symmetric matrices, graphs, paths, spectra 
@article{ELA_2010__21__a12,
     author = {Da Fonseca, C.M.},
     title = {A lower bound for the number of distinct eigenvalues of some real symmetric matrices},
     journal = {The electronic journal of linear algebra},
     pages = {3--11},
     publisher = {mathdoc},
     volume = {21},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2010__21__a12/}
}
TY  - JOUR
AU  - Da Fonseca, C.M.
TI  - A lower bound for the number of distinct eigenvalues of some real symmetric matrices
JO  - The electronic journal of linear algebra
PY  - 2010
SP  - 3
EP  - 11
VL  - 21
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2010__21__a12/
LA  - en
ID  - ELA_2010__21__a12
ER  - 
%0 Journal Article
%A Da Fonseca, C.M.
%T A lower bound for the number of distinct eigenvalues of some real symmetric matrices
%J The electronic journal of linear algebra
%D 2010
%P 3-11
%V 21
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2010__21__a12/
%G en
%F ELA_2010__21__a12
Da Fonseca, C.M. A lower bound for the number of distinct eigenvalues of some real symmetric matrices. The electronic journal of linear algebra, Tome 21 (2010), pp. 3-11. http://geodesic.mathdoc.fr/item/ELA_2010__21__a12/