On a Parametrization of Positive Semidefinite Matrices with Zeros [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a polynomial map associated with a simplicial complex supported on cliques of the graph.
Mathias Drton, Josephine Yu
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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
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Fischer Type Log-Majorization of Singular Values on Partitioned Positive Semidefinite Matrices
Journal of Function Spaces, 2021 In this paper, we establish a Fischer type log-majorization of singular values on partitioned positive semidefinite matrices, which generalizes the classical Fischer's inequality. Meanwhile, some related and new inequalities are also obtained.
Benju Wang, Yun Zhang
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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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Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices [PDF]
, 2020 This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite d × d matrices. In particular, for conservative and subcritical affine processes we show that a finite log-moment of the ...
Jonas Kremer +7 more
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TRACE INEQUALITIES OF POSITIVE SEMIDEFINITE MATRICES [PDF]
, 2006 In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated. The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang’s inequalities.
ÖZEL, Mustafa +3 more
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Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations [PDF]
, 1991 Elsner L, Mehrmann V. Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations. Numerische Mathematik.
Mehrmann, Volker, Elsner, Ludwig
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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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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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