Geodesic
Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 537-544.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
Classification : 05C50, 15A42, 15A48, 60J10
Keywords: eigenvalue; irreducible nonnegative matrix; averaged minimal cut 
@article{CMJ_2002__52_3_a7,
     author = {Zhang, Xiao-Dong and Luo, Rong},
     title = {Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {537--544},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2002},
     mrnumber = {1923259},
     zbl = {1014.15013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002__52_3_a7/}
}
TY  - JOUR
AU  - Zhang, Xiao-Dong
AU  - Luo, Rong
TI  - Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 537
EP  - 544
VL  - 52
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002__52_3_a7/
LA  - en
ID  - CMJ_2002__52_3_a7
ER  - 
%0 Journal Article
%A Zhang, Xiao-Dong
%A Luo, Rong
%T Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
%J Czechoslovak Mathematical Journal
%D 2002
%P 537-544
%V 52
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2002__52_3_a7/
%G en
%F CMJ_2002__52_3_a7
Zhang, Xiao-Dong; Luo, Rong. Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 537-544. http://geodesic.mathdoc.fr/item/CMJ_2002__52_3_a7/