On Cone of Nonsymmetric Positive
Yingnan Wang, Naihua Xiu, Ji-ye Han · 2010
In this paper, we analyze and characterize the cone of nonsymmetric positive semideflnite 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 P0-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 su‐cient and necessary conditions for a nonsymmetric matrix to be positive semideflnite are given. Finally, we present some properties of metric projection onto the NS-psd cone.