Results 41 to 50 of about 41,020 (249)
Hilbert’s 17th problem in free skew fields
Forum of Mathematics, Sigma, 2020 This paper solves the rational noncommutative analogue of Hilbert’s 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of Hermitian matrices in its domain, then it is a sum of Hermitian squares of noncommutative ...
Jurij Volčič
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Logarithmic barriers for sparse matrix cones
, 2012 Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with ...
Andersen, Martin S. +2 more
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On a decomposition of conditionally positive-semidefinite matrices
Linear Algebra and its Applications, 1981 AbstractA symmetric matrix C is said to be copositive if its associated quadratic form is nonnegative on the positive orthant. Recently it has been shown that a quadratic form x'Qx is positive for all x that satisfy more general linear constraints of the form Ax⩾0, x≠0 iff Q can be decomposed as a sum Q=A'CA+S, with Cstrictly copositive and S positive ...
M. J. D. Powell +2 more
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Products of positive semidefinite matrices
Linear Algebra and its Applications, 1988 AbstractWe characterize the complex square matrices which are expressible as the product of finitely many positive semidefinite matrices; a matrix T can be expressed as such if and only if det T⩾0; moreover, the number of factors can always be limited to five.
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Approximation by matrices positive semidefinite on a subspace
Linear Algebra and its Applications, 1988 AbstractWe obtain the best approximation to a matrix by matrices positive semidefinite on a subspace. As a by-product, we present two new characterizations of Euclidean distance matrices.
Jim Wells, T.L. Hayden
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有关矩阵广义逆的惯性指数及其应用(Inertia formulae related to the generalized inverse with applications)
Zhejiang Daxue xuebao. Lixue ban, 2019 In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse . Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices.
WUZhongcheng(吴中成) +1 more
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A quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices
, 2017 We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model.
Cerf, N. J. +2 more
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Rank inequalities for positive semidefinite matrices
Linear Algebra and its Applications, 1996 AbstractSeveral inequalities relating the rank of a positive semidefinite matrix with the ranks of various principal submatrices are presented. These inequalities are analogous to known determinantal inequalities for positive definite matrices, such as Fischer's inequality, Koteljanskii's inequality, and extensions of these associated with chordal ...
Wayne Barrett, Michael Lundquist
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Process Resilience under Optimal Data Injection Attacks
AIChE Journal, EarlyView.Abstract In this article, we study the resilience of process systems in an information‐theoretic framework, from the perspective of an attacker capable of optimally constructing data injection attacks. The attack aims to distract the stationary distributions of process variables and stay stealthy, simultaneously.
Xiuzhen Ye, Wentao Tang
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GBD and $ \mathcal{L} $-positive semidefinite elements in $ C^* $-algebras
AIMS MathematicsThis paper focused on the generalized Bott-Duffin (GBD) inverse and the $ {\rm GBD} $ elements in Banach algebra with involution and $ C^* $-algebra, as well as on the property of the $ p $-positive semidefinite elements that are a generalization of the $
Kezheng Zuo +2 more
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