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.
