how to proof the sabinvariance theorem?

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# how to proof the sabinvariance theorem?

Submitted by ycb17 on Fri, 05/07/2004 - 17:22

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the sabinvariance theorem:

Let T be a non-negative irreducible matrix,s a positve number.and y>=.=0.a vector satisfying Ty<=sy.

Then (a) y>0;(b)s>=r,where r is the Perron-Frobenius eigenvalue of T.

Moreover,s=r if and only if Ty=sy.

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