# how to determine transient and recurrent state from transition matrix

I wonder how can I determine the transient and recurrent state from transition matrix ? I mean if I have 10 states It would be very hard to draw diagram for them so how to analyse the matrix? For example consider : $$\begin{bmatrix} 0.1 & 0.2 & 0.7 & 0 \\ 0.7 & 0 & 0.2 & 0.1 \\ 0.6 & 0.4 & 0 & 0\\ 0 & 0.5 & 0.5 & 0 \end{bmatrix}$$ Can anyone tell me how to approach this problem I only want to know how to look at transition matrix and identify transient and recurrent states?

Thanks.

• Draw a picture. Only those places in the matrix with a nonzero entry matter. – Did Apr 12 '15 at 13:49
• I know this was 4 states problem what if I have 8 states then drawing picture is not very efficient method. I am looking for another method to identify states by solely looking at entries of matrix. – user59419 Apr 12 '15 at 18:21
• You may use the free software MCQueue that can be downloaded from personal.vu.nl/h.c.tijms The module for state classification is based on a classical paper of Fox and Landi in Commun. ACM 11 (1968), p. 619-621 – user164118 Apr 13 '15 at 10:47
• Thanks I am looking for method to approach these types of problem later like using this method in the exam,... – user59419 Apr 13 '15 at 15:12