Stability Matrices and the Solvability of Certain Systems of Linear Inequalities†
Simon A. Levin · Linear and Multilinear Algebra · 1974
Let A be a real n × nmatrix with non-negative non-diagonal elements aij(I ≠ j). Ais called a stability matrix if and only if all of its eigenvalues have strictly negative real parts. It is proved that A is a stability matrix if and only if the system Ax > 0, x > 0has no non-trivial solution. Further, one and only one of the systems Ax 0and Ax > 0, x > 0has a non-trivial solution