Results 11 to 20 of about 86 (84)
Notes and counterexamples on positive (semi) definite properties of some matrix products
Ain Shams Engineering Journal, 2018 In the present paper, we give some notes and counterexamples to show that the positive (semi) definite property of the Khatri-Rao and Tracy-Singh products of partitioned matrices are in general incorrect and show also that the matrix triangle inequality ...
Zeyad Al-Zhour
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An â„‹-tensor-based criteria for testing the positive definiteness of multivariate homogeneous forms
Open Mathematics, 2022 A positive definite homogeneous multivariate form plays an important role in the field of optimization, and positive definiteness of the form can be identified by a special structured tensor.
Bai Dongjian, Wang Feng
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New iterative codes for đť“—-tensors and an application
Open Mathematics, 2016 New iterative codes for identifying đť“— -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given.
Wang Feng, Sun Deshu
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A generalization of Kruskal’s theorem on tensor decomposition
Forum of Mathematics, Sigma, 2023 Kruskal’s theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called k-ranks of the product tensors are large.
Benjamin Lovitz, Fedor Petrov
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Open Mathematics, 2021 Positive definite polynomials are important in the field of optimization. â„‹-tensors play an important role in identifing the positive definiteness of an even-order homogeneous multivariate form.
Sun Deshu, Bai Dongjian
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Fast evaluation of nonlinear functionals of tensor product wavelet expansions [PDF]
, 2010 For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index
Christoph Schwab +5 more
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Open Mathematics, 2021 A higher dimensional generalization of the cross product is associated with an adequate matrix multiplication. This index-free view allows for a better understanding of the underlying algebraic structures, among which are generalizations of Grassmann’s ...
Lewintan Peter
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Bounds for the Z-eigenpair of general nonnegative tensors
Open Mathematics, 2016 In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented.
Liu Qilong, Li Yaotang
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Iterative solution of quadratic tensor equations for mutual polarisation
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 5, Page 301-312, 2002., 2002 To describe mutual polarisation in bulk materials containing high polarisability molecules, local fields beyond the linear approximation need to be included. A second order tensor equation is formulated, and it describes this in the case of crystalline or at least locally ordered materials such as an idealised polymer. It is shown that this equation is
Wynand S. Verwoerd
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Introduction to Grassmann manifolds and quantum computation
Journal of Applied Mathematics, Volume 2, Issue 8, Page 371-405, 2002., 2002 Geometrical aspects of quantum computing are reviewed elementarily for nonexperts and/or graduate students who are interested in both geometry and quantum computation. We show how to treat Grassmann manifolds which are very important examples of manifolds in mathematics and physics.
Kazuyuki Fujii
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