ALPS: Classes of stable and semipositive matrices

The purpose of this paper is to characterize and interrelate various degrees of stability and semipositivity for real square matrices. The standard conditions for three major classes of matrices are made both stronger and weaker, and the resulting classes are examined. The major classes are diagonally stable, stable, and semipositive matrices, denoted by $\text{A,L,}$ and $\text{S,}$ respectively. Their relationship to the classes of matrices whose principal minors are positive (denoted by $\text{P}$ and non-negative (denoted by $\text{P}$₀) is also presented.