Tensor rank –Symmetric tensor rank –Segre variety –Veronese varietyFix integers n ≥ 1, d ≥ 2. Let V be an (n + 1)-dimensional vector space over a field with characteristic zero. Fix a symmetric tensor T Sd(V) Vd{Tin S^d(V)subset V^{otimes d}}. Here we prove that the ...
Woo, Symmetric tensors: rank, Strassen's conjecture and e-computability, arXiv preprint:1506.03176, 2015.E. Carlini, M.V. Catalisano, L. Chiantini, A.V. Geramita, and Y. Woo, Symmetric tensors: rank, Strassen's conjecture and e-computability, arXiv:1506.03176 [math.AC], June 2015....
A numerical integrator is presented that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-dependent
Tensor[SymmetricProductsOfKillingTensors] - form all possible symmetric tensors of a given rank (linearly independent over the real numbers) from a list of symmetric tensors Calling Sequences SymmetricProducstOfKillingTensors( K , p , ptlist ) Parameters
作者: S Benenti 摘要: A general analysis of special classes of symmetric two-tensor on Riemannian manifolds is provided. These tensors arise in connection with special topics in differential geometry and analytical mechanics: geodesic equivalence and separation of variables. It is shown that they ...
symmetric tensorsranksLet n ≥ n be a natural number. Let Mn(K) be the ring of all n × n matrices over an arbitrary field K. In the present paper, we will find the description of all additive mappings T: Mn(K) → Mn(K) such that [T(y), y] = T(y)y - yT(y) = 0 ...
Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directio...
We derive several perturbative results that are relevant to the well-posedness of recovering rank-one structure from approximately-rank-one symmetric tensors. We also specialize the analysis of the shifted symmetric higher-order power method, an algorithm for computing symmetric tensor eigenvectors, to...
(NetworkAddressTranslation) The technology that maintains the privacy of the addresses of the computers in a home or business network when accessing the Internet. It converts the private addresses that are assigned to the internal computers to one or more public addresses that are visible on the ...
A Riemannian Newton Optimization Framework for the Symmetric Tensor Rank Approximation Problem We present an explicit and exact formula for the gradient vector and the Hessian matrix of the method, in terms of the weights and points of the low rank approximation and the symmetric tensor to approxima...