On The Structure Of Stochastic Matrices With A Subdominant Eigenvalue Near 1
- An nxn irreducible stochastic matrix P can possess
a subdominant eigenvalue near 1. In this
article we clarify the relationship between the nearness of these
eigenvalues and the nearly uncoupling (some authors say ``nearly completely
decomposable'') of P. We prove that for fixed n, if the subdominant eigenvalue is
sufficiently close to 1, then P is nearly uncoupled. We
then provide examples which show that the subdominant eigenvalue must, in general, be
remarkable close to 1 before such uncoupling occurs.
Prof. Meyer's work was supported in
part by the National Science Foundation under grants
DMS-9020915 and DMS-9403224.
- Linear Algebra and Its Applications
- Vol. 272, 1998, pp. 193-203
- D. J. Hartfiel
- Carl D. Meyer
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