Some classes of nonsingular matrices and applications

Motivated by conditions that arise from results on mean first passage times matrices in Markov chains, we consider here two classes of real matrices whose elements satisfy some of these conditions, or variation thereof, and which result in the nonsingularity of their elements. The conditions are quite distinct from Geršgorin circles-type conditions. Our results lead to a sufficient condition for matrices to have 1 as their unique positive eigenvalue.