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Answers for “为什么求解 $\pi P = \pi$ 会导致马尔可夫链中出现冗余方程?”

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The stationary distribution is the row vector π=[4/11,7/11]\pi = [4/11, 7/11].

Conditions: The transition matrix is P=[0.30.70.40.6]P = \begin{bmatrix} 0.3 & 0.7 \\ 0.4 & 0.6 \end{bmatrix}.; π\pi is a row vector satisfying πP=π\pi P = \pi and ∑πi=1\sum \pi_i = 1.

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A simple sanity check is to verify that the sum of the probabilities in each row of the transition matrix equals 1.

Conditions: The matrix is intended to be a transition matrix for a Markov chain.