Results 1 to 10 of about 849 (69)
An ℋ-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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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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New iterative codes for 𝓗-tensors and an application
Open Mathematics, 2016 New iterative codes for identifying 𝓗 -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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Open Mathematics, 2021 Positive definite polynomials are important in the field of optimization. ℋ-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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Plethysm and fast matrix multiplication [PDF]
, 2018 Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$.
Seynnaeve, Tim
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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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Effective identifiability criteria for tensors and polynomials [PDF]
, 2017 A tensor $T$, in a given tensor space, is said to be $h$-identifiable if it admits a unique decomposition as a sum of $h$ rank one tensors. A criterion for $h$-identifiability is called effective if it is satisfied in a dense, open subset of the set of ...
Massarenti, Alex +2 more
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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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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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A binary encoding of spinors and applications
Complex Manifolds, 2020 We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations.
Arizmendi Gerardo, Herrera Rafael
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