- #1
ha9981
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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 I am 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?
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?