The Perron-Frobenius theorem -- a proof with the use of Markov chains

DOI10.1007/S10958-009-9347-9zbMath1177.15009OpenAlexW2012436374MaRDI QIDQ1036977

Valentina S. Al'pina, Yurii A. Al'pin

Publication date: 13 November 2009

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-009-9347-9

zbMATH Keywords

Markov chainsergodic theoremPerron-Frobenius theoremirreducible nonnegative matrixmatrix graph

Mathematics Subject Classification ID

Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48)

Cites Work

• Non-negative matrices and Markov chains.
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