Results 11 to 20 of about 41,274 (203)
Matrices with high completely positive semidefinite rank
Linear Algebra and its Applications, 2017 A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite rank of $M$, and it is an open question whether there exists an upper bound on this number as a function of the ...
de Laat, David +2 more
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On Positive Semidefinite Matrices with Known Null Space [PDF]
SIAM Journal on Matrix Analysis and Applications, 2002 We show how the zero structure of a basis of the null space of a positive semidefinite matrix can be exploited to determine a positive definite submatrix of maximal rank. We discuss consequences of this result for the solution of (constrained) linear systems and eigenvalue problems.
Arbenz, Peter, Drmac, Zlatko
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Singular Values of Differences of Positive Semidefinite Matrices [PDF]
SIAM Journal on Matrix Analysis and Applications, 2001 Based on known results, the author shows relations between the singular values of two positive semidefinite matrices. Let \(A\) and \(B\) be complex positive semidefinite matrices of order \(n\) and let us denote as \(A \oplus B\) the block diagonal matrix with \(A\) and \(B\) on the diagonal. Using the common notation for singular values \(s_1(.) \geq
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On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings [PDF]
, 2015 We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+^n$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This cone has been
Burgdorf, Sabine +2 more
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Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone [PDF]
, 2015 We investigate the completely positive semidefinite cone $\mathcal{CS}_+^n$, a new matrix cone consisting of all $n\times n$ matrices that admit a Gram representation by positive semidefinite matrices (of any size).
Laurent, Monique, Piovesan, Teresa
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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
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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
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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
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Poisson Quantum Information [PDF]
Quantum, 2021 By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information.
Mankei Tsang
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Semidefinite descriptions of the convex hull of rotation matrices [PDF]
, 2014 We study the convex hull of $SO(n)$, thought of as the set of $n\times n$ orthogonal matrices with unit determinant, from the point of view of semidefinite programming. We show that the convex hull of $SO(n)$ is doubly spectrahedral, i.e. both it and its
Parrilo, Pablo A. +2 more
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