We define a transition matrix to have each entry nonnegative and each column sum to 1.
(a) Check that the three transition matrices shown in this Topic meet these two conditions. Must any transition matrix do so?
(b) Observe that if
is a transition matrix from
Show that a power of a transition matrix is also a transition matrix.
(c) Generalize the prior item by proving that the product of two appropriatelysized transition matrices is a transition matrix.