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A stochastic matrix (also termed probability matrix, transition matrix, substitution matrix, or Markov matrix) is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability.

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Follow up: Show that these vectors are linearly independent almost surely

This is not an answer, just a slightly different perspective on the original problem. If I understand your setup correctly, you have two families of hypersurfaces: those of the form $E_i(P)=\{x\in \m …
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