A characterization of nonnegativity relative to proper cones

2018/01/30 by Chandrashekaran Arumugasamy, Arumugasamy, Chandrashekaran, Sachindranath Jayaraman +3
Mathematics · #15B48 #90C33 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:15B48 #msc:90C33

paper · pdf · doi:10.48550/arxiv.1801.09849

In this updated version, we have corrected some minor typos from the earlier version

arxiv created 2019/05/21 · arxiv updated 2019/05/22

Abstract

Let A be an m × n matrix with real entries. Given two proper cones K₁ and K₂ in ℝⁿ and ℝ^m, respectively, we say that A is nonnegative if A(K₁) ⊆ K₂. A is said to be semipositive if there exists a x ∈ K₁^∘ such that Ax ∈ K₂^∘. 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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