This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear system only if the measurement matrix has a row-span intersecting the positive orthant. Focusing on two types of binary measurement matrices, Bernoulli 0-1 ma...

We study matrix inequalities involving partial traces for positive semidefinite block matrices. First of all, we present a new method to prove celebrated result Choi [Linear Algebra Appl. 516 (2017)]. Our also allows us generalization another Multilinear 66 (2018)]. Furthermore, shall give an improvement on recent Li, Liu and Huang [Operators Matrices 15 (2021)]. In addition, include with some ...

The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal...

We first give an Oppenheim type determinantal inequality for the Khatri-Rao product of two block positive semidefinite matrices, and then we extend our result to multiple matrices. As products, extensions inequalities Hadamard are also included.

In this paper, the equivalence of the existence of unique real and complex A-invariant semidefinite subspaces for real H-positive real matrices are shown.

We compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions, in terms of integrals related to Mehta’s integral. Several applications for the probabilistic analysis of semidefinite programming are given. AMS subject classifications: 15B48, 52A55, 53C65, 60D05, 90C22