On Cone of Nonsymmetric Positive Semidefinite Matrices

Wang Yingnan (wyn1982hotmail.com)
Xiu Naihua (nhxiubjtu.edu.cn)
Han Jiye (jiyehanvip.sina.com)

Abstract: In this paper, we analyze and characterize the cone of nonsymmetric positive semidefinite matrices (NS-psd). Firstly, we study basic properties of the geometry of the NS-psd cone and show that it is a hyperbolic but not homogeneous cone. Secondly, we prove that the NS-psd cone is a maximal convex subcone of $P_0$-matrix cone which is not convex. But the interior of the NS-psd cone is not a maximal convex subcone of $P$-matrix cone. As the byproducts, some new sufficient and necessary conditions for a nonsymmetric matrix to be positive semidefinite are given. Finally, we present some properties of metric projection onto the NS-psd cone.

Keywords: Nonsymmetric positive semidefinite matrix,hyperbolic cone, facial structure, maximal convex subcone,$P_0$-matrix, projection

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Other Topics

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Entry Submitted: 06/28/2009
Entry Accepted: 06/29/2009
Entry Last Modified: 03/30/2010

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