Results 41 to 50 of about 49,764 (200)
Exposed faces of semidefinitely representable sets
, 2009 A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite.
Netzer, Tim +2 more
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Real factorization of positive semidefinite matrix polynomials
Linear Algebra and its ApplicationsSuppose $Q(x)$ is a real $n\times n$ regular symmetric positive semidefinite matrix polynomial. Then it can be factored as $$Q(x) = G(x)^TG(x),$$ where $G(x)$ is a real $n\times n$ matrix polynomial with degree half that of $Q(x)$ if and only if $\det(Q(x))$ is the square of a nonzero real polynomial.
Sarah Gift, Hugo J. Woerdeman
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Applied Set-Valued Analysis and Optimization, 2023 We present an algorithm for computing the minimum-rank positive semidefinite completion of a sparse matrix with a chordal sparsity pattern. This problem is tractable, in contrast to the minimum-rank positive semidefinite completion problem for general sparsity patterns.
Jiang, Xin +3 more
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MathematicsThis article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality.
Hongli Yang +3 more
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Refined Upper Solution Bound of the Continuous Coupled Algebraic Riccati Equation
Complexity, 2020 The continuous coupled algebraic Riccati equation (CCARE) has wide applications in control theory and linear systems. In this paper, by a constructed positive semidefinite matrix, matrix inequalities, and matrix eigenvalue inequalities, we propose a new ...
Li Wang
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Generalized Randić Estrada Indices of Graphs
Mathematics, 2022 Let G be a simple undirected graph on n vertices. V. Nikiforov studied hybrids of AG and DG and defined the matrix AαG for every real α∈[0,1] as AαG=αDG+(1−α)AG.
Eber Lenes +3 more
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A Class of Weighted Low Rank Approximation of the Positive Semidefinite Hankel Matrix
Journal of Applied Mathematics, 2015 We consider the weighted low rank approximation of the positive semidefinite Hankel matrix problem arising in signal processing. By using the Vandermonde representation, we firstly transform the problem into an unconstrained optimization problem and then
Jianchao Bai +3 more
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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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Inequalities for selected eigenvalues of the product of matrices
, 2019 The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues.
Xi, Bo-Yan, Zhang, Fuzhen
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Positive semidefinite solution to matrix completion problem and matrix approximation problem
Filomat, 2022 In this paper, firstly, we discuss the following matrix completion problem in the spectral norm: ?(A B B* X)?2 < 1 subject to (A B B* X) ? 0. The feasible condition for the above problem is established, in this case, the general positive semidefinite solution and its minimum rank are presented.
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