Results 91 to 100 of about 41,274 (203)
, 2015 The study of entrywise powers of matrices was originated by Loewner in the pursuit of the Bieberbach conjecture. Since the work of FitzGerald and Horn (1977), it is known that $A^{\circ \alpha} := (a_{ij}^\alpha)$ is positive semidefinite for every ...
Guillot, Dominique +2 more
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Positive semidefiniteness of estimated covariance matrices in linear models for sample survey data
Special Matrices, 2016 Descriptive analysis of sample survey data estimates means, totals and their variances in a design framework. When analysis is extended to linear models, the standard design-based method for regression parameters includes inverse selection probabilities ...
Haslett Stephen
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On vector configurations that can be realized in the cone of positive matrices
, 2010 Let $v_1$,..., $v_n$ be $n$ vectors in an inner product space. Can we find a natural number $d$ and positive (semidefinite) complex matrices $A_1$,..., $A_n$ of size $d \times d$ such that ${\rm Tr}(A_kA_l)= $ for all $k,l=1,..., n$? For such matrices to
Frenkel, Péter E., Weiner, Mihály
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From ƒ-Divergence to Quantum Quasi-Entropies and Their Use
Entropy, 2010 Csiszár’s ƒ-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting, positive semidefinite matrices are in the place of probability distributions and the quantum generalization is called ...
Dénes Petz
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Hyperbolic Polynomials and Generalized Clifford Algebras [PDF]
, 2012 We consider the problem of realizing hyperbolicity cones as spectrahedra, i.e. as linear slices of cones of positive semidefinite matrices. The generalized Lax conjecture states that this is always possible. We use generalized Clifford algebras for a new
Netzer, Tim, Thom, Andreas
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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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Journal of Numerical Analysis and Approximation Theory, 2010 In this paper, we obtain new results concerning the generalizations of additive and multiplicative majorizations by means of exponential convexity. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type ...
Naveed Latif, Josip Pečarić
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Mokslas: Lietuvos Ateitis, 2015 Semidefinite Programming (SDP) is a fairly recent way of solving optimization problems which are becoming more and more important in our fast moving world. It is a minimization of linear function over the intersection of the cone of positive semidefinite
Rasa Giniūnaitė
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Regression on fixed-rank positive semidefinite matrices: a Riemannian approach [PDF]
, 2011 The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems.
Bonnabel, Silvere +2 more
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Mixed discriminants of positive semidefinite matrices
Linear Algebra and its Applications, 1989 If \(A^ k=(a^ k_{ij})\) are \(n\times n\) complex matrices \(k=1,2,...,n\), then their mixed discriminant \(D(A^ 1,...,A^ n)\) is \(\frac{1}{n!}\sum_{\sigma \in S_ n}\det (a_{ij}^{\sigma (j)})\), where \(S_ n\) is the symmetric group of degree n. If all the \(A^ k\) are equal this turns out to be det A, whereas if each \(A^ k\) is a diagonal matrix the
openaire +1 more source