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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

A transition matrix is called regular if some power of it has all entries strictly positive. For M=(01/211/2)M = \begin{pmatrix} 0 & 1/2 \\ 1 & 1/2 \end{pmatrix} (columns sum to 11), what is the smallest positive integer kk such that every entry of MkM^k is positive?