A transition matrix is a square matrix used to describe the transitions of a Markov chain.

The term "transition matrix" is used in a number of different contexts in mathematics.

In linear algebra, it is sometimes used to mean a change of coordinates matrix.

In the theory of Markov chains, it is used as an alternate name for for a stochastic matrix, i.e., a matrix that describes transitions.

In control theory, a state-transition matrix is a matrix whose product with the initial state vector gives the state vector at a later time.

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