Each of the T factors in Equation 3 is independent of the instant t, as per the notation in (Rabiner, 1989).
each factor is a function only of the state S i in which the conversation was at time t − 1 and the state S j in which the conversation is at time t, and not of the instants t − 1 or t. It may be expressed as the scalar a ij which forms the ith row and jth column entry of the matrix {a ij } ≡ Θ.