Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
Czechoslovak Mathematical Journal (2002)
- Volume: 52, Issue: 3, page 537-544
- ISSN: 0011-4642
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topZhang, Xiao-Dong, and Luo, Rong. "Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices." Czechoslovak Mathematical Journal 52.3 (2002): 537-544. <http://eudml.org/doc/30722>.
@article{Zhang2002,
abstract = {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.},
author = {Zhang, Xiao-Dong, Luo, Rong},
journal = {Czechoslovak Mathematical Journal},
keywords = {eigenvalue; irreducible nonnegative matrix; averaged minimal cut; eigenvalue; irreducible nonnegative matrix; averaged minimal cut; Laplacian matrices; weighted graphs; Markov chains},
language = {eng},
number = {3},
pages = {537-544},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices},
url = {http://eudml.org/doc/30722},
volume = {52},
year = {2002},
}
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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 537
EP - 544
AB - 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.
LA - eng
KW - eigenvalue; irreducible nonnegative matrix; averaged minimal cut; eigenvalue; irreducible nonnegative matrix; averaged minimal cut; Laplacian matrices; weighted graphs; Markov chains
UR - http://eudml.org/doc/30722
ER -
References
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- 10.1016/0012-365X(92)90288-Q, Discrete Math. 109 (1992), 171–183. (1992) Zbl0783.05073MR1192380DOI10.1016/0012-365X(92)90288-Q
- Note on the fundamental theorem on irreducible nonnegative matrices, Proc. Edinburgh Math. Soc. 12 (1960/1961), 107–112. (1960/1961)
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