Results 11 to 20 of about 71,699 (272)
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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SIAM Journal on Matrix Analysis and Applications, 2020 This paper explores the well-known identification of the manifold of rank $p$ positive-semidefinite matrices of size $n$ with the quotient of the set of full-rank $n$-by-$p$ matrices by the orthogo...
Estelle Massart, Pierre-Antoine Absil
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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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Monotonicity of positive semidefinite Hermitian matrices [PDF]
Proceedings of the American Mathematical Society, 1972 Inequalities which compare elements of the convex cone of positive semidefinite hermitian matrices with products of roots of elements are proved. They yield inequalities for Schur functions (generalized matrix functions) which, when specialized to the determinant, give a result of R. Bellman and L. Mirsky.
Russell Merris, Stephen Pierce
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Correlation matrices, Clifford algebras, and completely positive semidefinite rank [PDF]
Linear and multilinear algebra, 2017 A symmetric matrix X is completely positive semidefinite (cpsd) if there exist positive semidefinite matrices (for some ) such that for all . The of a cpsd matrix is the smallest for which such a representation is possible.
Anupam Prakash, Antonios Varvitsiotis
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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]
, 2016 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.
Ehler, M, Graef, M, Kiraly, FJ
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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 ...
N. Eagambaram
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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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