On Nonnegative Solutions of Matrix Equations
H. D. Victory · SIAM Journal on Algebraic and Discrete Methods · 1985
Let ${\bf A}$ be a nonnegative and nontrivial $n \times n$ matrix. In this work, we present necessary and sufficient conditions for the matrix equation, $( \lambda {\bf I} - {\bf A} ) x = b$, to possess a nonnegative solution x whenever b is a given nonnegative and nontrivial vector and $\lambda$ is any given positive parameter. This analysis extends a result of S. Friedland and H. Schneider (SIAM J. Alg. Disc. Meth., 2 (1980), Thm. 7.1, pp. 185–200).