A Characterization of Nonnegativity Relative to Proper Cones

Chandrashekaran Arumugasamy (), Sachindranath Jayaraman () and Vatsalkumar N. Mer ()
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Chandrashekaran Arumugasamy: Central University of Tamil Nadu
Sachindranath Jayaraman: Indian Institute of Science Education and Research Thiruvananthapuram
Vatsalkumar N. Mer: Indian Institute of Science Education and Research Thiruvananthapuram

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 935-944

Abstract: Abstract Let A be an m × n matrix with real entries. Given two proper cones K1 and K2 in ℝn and ℝm, respectively, we say that A is nonnegative if A(K1) ⊆ K2. A is said to be semipositive if there exists a $$x \in K_1^ \circ $$ x ∈ K 1 ∘ such that $$Ax \in K_2^ \circ $$ A x ∈ K 2 ∘ . 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.

Keywords: Semipositivity of matrices; nonnegative matrices; proper cones; semipositive cone.; 15B48; 90C33 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0442-4

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