Eigenvalues of the matrix $(I-P)$ Let $P$ be a strictly positive $n\times n$ stochastic matrix. 
I hope to find out the stability of a system characterized by the matrix $(I-P)$. So I'm interested in knowing under what condition on the entries of $P$ do all the eigenvalues of the matrix $(I-P)$ lie (not necessarily strictly) within the unit disk in the complex plane? The set of eigenvalues of $P$ is shifted by $(1-\sigma(P))$, which would require additional conditions to be placed on $P$ so as to keep them within the unit disk.
Or can anybody point out a direction towards which I can look for the answer? I don't really know what subject of linear algebra I should go for...

One sufficient condition (that is not necessary) is that all diagonal entries of $P$ are greater than or equal to $1/2$. If this is the case, by Gersgorin disc theorem, all eigenvalues of $I-P$ will lie inside the closed disc centered at $1/2$ with radius $1/2$, and hence lie inside the closed unit disc as well.
