๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On cone of nonsymmetric positive semidefinite matrices

โœ Scribed by Yingnan Wang; Naihua Xiu; Jiye Han

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
252 KB
Volume
433
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

A nonpolyhedral cone of class function i
A nonpolyhedral cone of class function inequalities for positive semidefinite matrices
โœ Wayne Barrett; H. Tracy Hall; Raphael Loewy ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 150 KB

A function f from the symmetric group S n into R is called a class function if it is constant on each conjugacy class. Let d f be the generalized matrix function associated with f, mapping the n-by-n Hermitian matrices to R. For example, if f (ฯƒ ) = sgn(ฯƒ ), then d f (A) = det A. Let K n (K n (R)) d

On a product of positive semidefinite ma
On a product of positive semidefinite matrices
โœ A.R. Meenakshi; C. Rajian ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 59 KB

two psd matrices is psd if and only if the product is normal.