Results 21 to 30 of about 54,917 (203)
Sufficient conditions to be exceptional
Special Matrices, 2016 A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A
Johnson Charles R., Reams Robert B.
doaj +1 more source
An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices
Special Matrices, 2021 A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.
Hutchinson George
doaj +1 more source
Positive semidefinite germs on the cone [PDF]
Pacific Journal of Mathematics, 2002 We show that any positive semidefinite analytic function germ on the cone z(2) = x(2) + y(2) is a sum of two squares of analytic function germs.
Fernando Galván, José Francisco +1 more
openaire +4 more sources
Positive Semidefinite Matrices, Exponential Convexity for Majorization, and Related Cauchy Means
Journal of Inequalities and Applications, 2010 We prove positive semidefiniteness of matrices generated by differences deduced from majorization-type results which implies exponential convexity and log-convexity of these differences and also obtain Lyapunov's and Dresher's inequalities for ...
N. Latif +2 more
doaj +2 more sources
Separability for mixed states with operator Schmidt rank two [PDF]
Quantum, 2019 The operator Schmidt rank is the minimum number of terms required to express a state as a sum of elementary tensor factors. Here we provide a new proof of the fact that any bipartite mixed state with operator Schmidt rank two is separable, and can be ...
Gemma De las Cuevas +2 more
doaj +1 more source
Low-rank matrix approximations over canonical subspaces
Journal of Numerical Analysis and Approximation Theory, 2020 In this paper we derive closed form expressions for the nearest rank-\(k\) matrix on canonical subspaces. We start by studying three kinds of subspaces. Let \(X\) and \(Y\) be a pair of given matrices. The first subspace contains all the \(m\times
Achiya Dax
doaj +7 more sources
A new look at nonnegativity on closed sets and polynomial optimization [PDF]
, 2011 We first show that a continuous function f is nonnegative on a closed set $K\subseteq R^n$ if and only if (countably many) moment matrices of some signed measure $d\nu =fd\mu$ with support equal to K, are all positive semidefinite (if $K$ is compact $\mu$
Lasserre, Jean B.
core +3 more sources
Analysis of Fixing Nodes Used in Generalized Inverse Computation
Advances in Electrical and Electronic Engineering, 2014 In various fields of numerical mathematics, there arises the need to compute a generalized inverse of a symmetric positive semidefinite matrix, for example in the solution of contact problems.
Pavla Hruskova
doaj +1 more source
POSITIVE SEMIDEFINITENESS OF DISCRETE QUADRATIC FUNCTIONALS [PDF]
Proceedings of the Edinburgh Mathematical Society, 2003 AbstractWe consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm–Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood ...
Bohner, Martin +2 more
openaire +2 more sources
Conditions for Existence of Dual Certificates in Rank-One Semidefinite Problems [PDF]
, 2014 Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate.
Hand, Paul
core +1 more source