Quadratic vector equations

Abstract

In this chapter, we aim to study in an unified fashion several quadratic vector and matrix equations with nonnegativity hypotheses. Specific cases of these problems have been studied extensively in the past by several authors. For references to the single equations and results, we refer the reader to the following sections, in particular Section 2.3. Many of the results appearing here have already been proved for one or more of the single instances of the problems, resorting to specific characteristics of the problem. In some cases the proofs we present here are mere rewritings of the original proofs with a little change of notation to adapt them to our framework, but in some cases we are effectively able to remove some hypotheses and generalize the results by abstracting the specific aspects of each problem.