Results 11 to 20 of about 71,800 (235)
AIMS Mathematics, 2023 We investigate the Riccati matrix equation $ X A^{-1} X = B $ in which the conventional matrix products are generalized to the semi-tensor products $ \ltimes $. When $ A $ and $ B $ are positive definite matrices satisfying the factor-dimension condition,
Pattrawut Chansangiam, Arnon Ploymukda
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Restricted Riemannian geometry for positive semidefinite matrices [PDF]
Linear Algebra and its Applications, 2021 A. Martina Neuman, Yuying Xie, Qiang Sun
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Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices [PDF]
, 2015 As a generalization of the standard phase retrieval problem,we seek to reconstruct symmetric rank- 1 matrices from inner products with subclasses of positive semidefinite matrices.
M. Ehler, Manuel Graef, F. Király
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Disjoint sections of positive semidefinite matrices and their applications in linear statistical models [PDF]
Special MatricesGiven matrices AA and BB of the same order, AA is called a section of BB if R(A)∩R(B−A)={0}{\mathscr{R}}\left(A)\cap {\mathscr{R}}\left(B-A)=\left\{0\right\} and R(AT)∩R((B−A)T)={0}{\mathscr{R}}\left({A}^{T})\cap {\mathscr{R}}\left({\left(B-A)}^{T ...
Eagambaram N.
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Inertia of partial transpose of positive semidefinite matrices [PDF]
Journal of Physics A: Mathematical and Theoretical, 2023 We show that the partial transpose of 9×9 positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4) . It solves an open problem in ‘LINEAR AND MULTILINEAR ALGEBRA. Changchun Feng et al, 2022’.
Yixuan Liang +3 more
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Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem [PDF]
The Electronic Journal of Linear Algebra, 2022 Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, have been extended to the case of symplectic ...
N. T. Son, T. Stykel
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Low-rank matrix approximations over canonical subspaces
Journal of Numerical Analysis and Approximation Theory, 2020 In this paper we derive closed form expressions for the nearest rank-\(k\) matrix on canonical subspaces. We start by studying three kinds of subspaces. Let \(X\) and \(Y\) be a pair of given matrices. The first subspace contains all the \(m\times
Achiya Dax
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New properties for certain positive semidefinite matrices [PDF]
, 2016 Minghua Lin
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Hyperbolic Relaxation of $k$-Locally Positive Semidefinite Matrices [PDF]
SIAM Journal on Optimization, 2020 In order to solve positive semidefinite (PSD) programs efficiently, a successful computational trick is to consider a relaxation, where PSD-ness is enforced only on a collection of submatrices. In order to study this formally, we consider the class of $n\
Grigoriy Blekherman +3 more
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On Some Matrix Trace Inequalities
Journal of Inequalities and Applications, 2010 We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices. Then, we obtain a trace inequality for products of two positive semidefinite block matrices by using 2×2 ...
Ramazan Türkmen +1 more
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