I used the equation Sn=T^-1 (Sn+1 -F) to work backwards and find the previous month from a transition matrix, but my values end up being large numbers, as well as a negative value. How do I interpret these values from here?
Edit: These are the workings for further clarifications. I do not understand how to interpret these values, especially the negative result.
Without more details it's not clear what's going on here, but it's quite possible that your transition matrix is ill-conditioned. If so, you can't "interpret these values".