Matrix-matrix multiplication forms each result entry from the dot product of a row in one matrix and a column in another. In Markov analysis, multiplying a transition matrix by itself produces a two-period transition matrix. section 11.2.2
The operation supports two equivalent forecasting routes:
- Compute the next state distribution repeatedly: multiply the current probability vector by P, then multiply the result by P again. section 11.2.2
Two-period cellular-market forecast
With NumPy, P2 = np.dot(P, P) gives the two-period transition matrix. Multiplying pi_0 by P2 yields [0.39012, 0.31454, 0.22803, 0.06731], matching the iterative forecast.
