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The state transition matrix can be viewed as the dynamics of the Markov chain because the probability distribution of the state at any time t+1, Pr(Xt​), can be uniquely determined by the probability distribution of the state at the previous time t and the state transition matrix, satisfying the relationship: Pr(Xt+1​=j)=∑i=1N​pij​⋅Pr(Xt​=i), where i,j∈X are arbitrary states in X, and N=#(X), the total number of states in X.

The [[Transitional Probability Matrix]] can be viewed as the [[Dynamics]] of the [[Markov Chain]] because the probability distribution of the state at any time [math]t+1[/math], [math]Pr(X_t)[/math], can be uniquely determined by the state probability distribution at the previous moment, i.e., [math]Pr(X_t)[/math] and [[Transitional Probability Matrix]], satisfying the relation:

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Pr(X_{t+1}=j)=\sum_{i=1}^N p_{ij}\cdot Pr(X_t=i),

Pr(X_{t+1}=j)=\sum_{i=1}^N p_{ij}\cdot Pr(X_t=i),

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The following table presents three different transition probability matrices and their EI values:

The following table presents three different transition probability matrices and their EI values: