Linear system with only positive solutions
I'm involved in the dimensioning of a markov chain.
In order to find its state probabilities I have constructed a system of equation, resulting in a sparse matrix of coefficients of the type Ax = b.
The problem is that when I solve the system (the solutions are correct, I already checked it), some states have negative solutions (which means that the probability of being in these states are negative (Headbang)).
Is there any rule/condition/property that the matrix A must have in order to obtain only Zero or Positive solutions?
Thanks in advance,