Question

An irreducible matrix does not have to be regular

Answer 1

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The definition that I have of a Transition Matrix for a Markov Chain is:

A transition matrix is regular if some power of it is positive.

Doesn't this mean though that in theory, you could keep calculating powers forever, because at some point one of the future transition matrices could become positive (assuming it's not already)?

Is there a more exact way checking? I have a transition matrix that I need to show is non-regular. For all the powers I've tried, it contains a 0, but for all I know, that could change if I kept checking forever.

The matrix:

⎡⎣⎢0.700.20100.300.8⎤⎦⎥