Jabarkan called the transition matrix, dari Ranté Markov dalam bahasa sunda

with the (i, j)'th element equal to

(In this formulation, element (i, j) is the probability of a transition from j to i.

An equivalent formulation is sometimes given with element (i, j) equal to the probability of a transition from i to j.

In that case the transition matrix is just the transpose of the one given here.)

For a discrete state space,

the integrations in the k-step transition probability are summations,

and can be computed as the k'th power of the transition matrix.

That is, if P is the one-step transition matrix, then

Pk is the transition matrix for the k-step transition.

Writing P for the transition matrix,

a stationary distribution is a vector which satisfies the equation

In this case, the stationary distribution is an eigenvector of the transition matrix,

associated with the eigenvalue 1.

If the transition matrix P is positive recurrent, irreducible, and aperiodic,

then Pk converges elementwise to a matrix in which éach column is the unique stationary distribution.

A transition matrix which is positive (that is, every element of the matrix is positive)

is irreducible, aperiodic, and positive recurrent.

A matrix is a stochastic matrix if and only if it is the matrix of transition probabilities of some Markov chain.