Our proof is built on Perron-Frobenius theorem, a seminal work in matrix theory (Meyer 2000). By Perron-Frobenius theorem, the power iteration algorithm for predicting top K persuaders converges to a unique C and this convergence is independent of the initialization of C if the persuasion probability matrix P is nonnegative, irreducible, and aperiodic (Heath 2002). We first show that P is nonne...

We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron-Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate r...

The aim of this manuscript is to understand the dynamics products nonnegative matrices. We extend a well known consequence Perron-Frobenius theorem on periodic points matrix finitely many matrices associated word and later word, possibly infinite length.

in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.

We present a new approach of proving certain Carath\'{e}odory-type theorems using the Perron-Frobenius Theorem, classical result in matrix theory describing largest eigenvalue with positive entries. One problems left open this note is whether our may be extended to prove similar results area, particular Colourful Carath\'{e}odory Theorem.