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On the structure of stochastic matrices with a subdominant eigenvalue near 1

✍ Scribed by D.J. Hartfiel; Carl D. Meyer

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
443 KB
Volume
272
Category
Article
ISSN
0024-3795

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✦ Synopsis

An n X n irreducible stochastic matrix P can possess a subdominant eigenvalue. say h,(P), near h = I. In this article we clarify the relationship between the nearness of these eigenvalues and the near-uncoupling (some authors say "nearly completelydecomposable") of P. We prove that for fixed n, if h,(P) is sufficiently close to A = 1, then P is nearly uncoupled. We then provide examples which show that h,(P) must, in general, be remarkably close to I before such uncoupling occurs. 0 3998 Elsevier Science Inc.

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