I assume so — I ask in the context of defining an irreducible set. If a set is non-irreducible, you should be able to find a "smaller" Markov chain matrix nested within a larger one. That "smaller" chain matrix has to be square?
2026-03-26 06:20:03.1774506003
Do the matrices representing Markov chains need to be square?
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The short answer is yes, because we account for the possibility of moving from any state to any state (and write a zero if this transition is not possible). This gives us $n \times n$ elements, which is a square matrix.