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arXiv · 1801.09849

A characterization of nonnegativity relative to proper cones

Chandrashekaran Arumugasamy·Sachindranath Jayaraman·Vatsalkumar N. Mer
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Abstract

Let $A$ be an $m \times n$ matrix with real entries. Given two proper cones $K_1$ and $K_2$ in $\mathbb{R}^n$ and $\mathbb{R}^m$, respectively, we say that $A$ is nonnegative if $A(K_1) \subseteq K_2$. $A$ is said to be semipositive if there exists a $x \in K_1^\circ$ such that $Ax \in K_2^\circ$. We prove that $A$ is nonnegative if and only if $A+B$ is semipositive for every semipositive matrix $B$. Applications of the above result are also brought out.

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Chandrashekaran Arumugasamy, Sachindranath Jayaraman, Vatsalkumar N. Mer. 2018-01-30. A characterization of nonnegativity relative to proper cones. https://arxiv.org/abs/1801.09849

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