Relationship between Compartmental Matrices, M-Matrices, and Markov Chains with Application in Economics

This paper presents necessary and sufficient conditions and an algorithm for a matrix A ∈ Rn×n to be written as A = −D−1KD, where K is a compartmental matrix and D is positive diagonal. This class of "compartmental related" matrices A is closely related to both M-matrices and Markov chains. The main purpose is to bridge the gap between compartmental models and other models, some arising in economics, without the preservation of mass property.