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We say that a stochastic matrix is regular iff $\exists n\in \mathbb N$ such that $p_{ij}(n)>0$ for all states $i,j$

How many powers of a matrix do we need to compute at most in order to verify that it is regular?

I think that we need to compute $n$ powers of the matrix but I don´t know if this is actually correct

I would appreciate if you can help me with this question

user128422
  • 3,057
  • Is $n$ the size of the matrix? – Ben Grossmann Apr 29 '16 at 04:29
  • Hint: if the chain is irreducible, what is the maximum possible distance between two states? If the chain is periodic, how does the period relate to the number of states? – Ben Grossmann Apr 29 '16 at 04:32
  • @Omnomnomnom, please look at my "similar" question, which has till now received no answer or comment on my approach. That question, if answered, will answer this one: http://math.stackexchange.com/questions/1762388/for-a-finite-state-irreducible-aperiodic-mc-show-that-pd2-has-all-coordin – Landon Carter Apr 29 '16 at 06:58
  • You can find the answer here: http://math.stackexchange.com/questions/450090/if-p-is-a-regular-transition-probability-matrix-then-pn2-has-no-zero-ele/450135#450135 –  Apr 30 '16 at 22:59

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