2023/03/01 by Aritra Narayan Hisabia, Hisabia, Aritra Narayan, Manideepa Saha +1
Computer Science · Mathematics · #15B10 #15B48 #52A20 #Advanced Topics in Algebra #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2303.00558
openalex publication_date 2023/03/01 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28
Given a proper cone K in the Euclidean space ℝn, a square matrix A is said to be K-semipositive if there exists an x∈ K such that Ax∈ int(K), the topological interior of K. The paper aims to study algebraic and geometrical properties of K-semipositive matrices with special emphasis on the self-dual proper Lorentz cone Ln+=\x∈ ℝn:xn≥ 0,∑i=1n-1xi2≤ xn2\. More specifically, we discuss a few necessary and other sufficient algebraic conditions for Ln+-semipositive matrices. Also, we provide algebraic characterizations for diagonal and orthogonal Ln+-semipositive matrices. Furthermore, given a square matrix A and a proper cone K, geometric properties of the semipositive cone KA,K=\x∈ K:~Ax∈ K\ and the cone of SA,K=\x:Ax∈ K\ are discussed in terms of their extremals. As Ln+ is an ellipsoidal cone, at last we find results for the cones KA,Ln+ and SA,Ln+ to be ellipsoidal.