Results 21 to 30 of about 41,020 (249)
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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On the cone of positive semidefinite matrices
Linear Algebra and its Applications, 1987 AbstractA survey of some general properties of the cone of positive semidefinite matrices, its faces, two isometric isomorphisms, and linear transformations on it is given.
Steven R. Waters, Richard D. Hill
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A class of positive semidefinite matrices
Linear Algebra and its Applications, 1987 AbstractA matrix [aij(α)xij] is shown to be positive semidefinite or positive definite if the matrix [xij] is positive semidefinite or positive definite and aij(α) belongs to a large class of functions of α. This class includes the reciprocals of the αth mean values of xii and xjj in the cases where xii, xjj, and α are all positive.
A.M. Russell, C.J.F. Upton
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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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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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On a product of positive semidefinite matrices
Linear Algebra and its Applications, 1999 AbstractNecessary and sufficient conditions are given for the product of two positive semidefinite (psd) matrices to be EP. As a consequence, it is shown that the product of two psd matrices is psd if and only if the product is normal.
C. Rajian, A.R. Meenakshi
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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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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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A New Algorithm for Positive Semidefinite Matrix Completion
Journal of Applied Mathematics, 2016 Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and low-rank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control.
Fangfang Xu, Peng Pan
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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 these ...
Latif N, Pečarić J, Anwar M
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