Displaying similar documents to “Characterizations of embeddable 3 × 3 stochastic matrices with a negative eigenvalue.”

Transforming stochastic matrices for stochastic comparison with the st-order

Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2010)

RAIRO - Operations Research

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We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.

Technical comment. A problem on Markov chains

Franco Giannessi (2010)

RAIRO - Operations Research

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A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.

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

Xiao-Dong Zhang, Rong Luo (2002)

Czechoslovak Mathematical Journal

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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.