Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices

Authors: Zhang X-D.1; Luo R.2

Source: Czechoslovak Mathematical Journal, Volume 52, Number 3, September 2002 , pp. 537-544(8)

Publisher: Springer

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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.

Keywords: eigenvalue; irreducible nonnegative matrix; averaged minimal cut

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, Peoples Republic of China, xdzhang2@hotmail.com 2: Department of Mathematics, West Virginia University, Morgantown, WV, 26505, U.S.A., luor@math.wvu.edu

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