I have to learn a section from my textbook and I can't seem to undertand what a regular transition matrix is. The definition given is: A transition matrix is regular if some integer power of it has all positive entries. Now an identity matrix isn't regular, but im pretty sure all integer powers of it have positive entries. I mean no transition matrix I have seen so far is negative except for (1-P) matrices. P = 0.2 0.1 0.7 0.6 0.4 0.2 0.2 0.5 0.1 for this matrix, is it regular because all values in it are positive and so all integer powers of P will remain positive? Do I have to mention that all rows add up to 1, is that important in being a regular matrix? also, how would u test to prove a transition matrix isn't regular?