On cone of nonsymmetric positive semidefinite matrices |
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Authors: | Yingnan Wang Naihua Xiu |
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Affiliation: | a Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, PR China b Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China |
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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 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 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. |
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Keywords: | 52A20 90C25 |
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