منابع مشابه
Engel Conditions and Symmetric Tensors
In a recent study of Engel Lie rings, Serena Cicalò and Willem de Graaf have given a practical set of conditions for an additively finitely generated Lie ring L to satisfy an Engel condition. We present a simpler and more direct proof of this fact. Then we generalize it to a result in the language of tensor algebra, which can be applied to other contexts.
متن کاملSymmetric nonnegative tensors and copositive tensors
Article history: Received 6 December 2012 Accepted 11 March 2013 Available online 8 April 2013 Submitted by R.A. Brualdi AMS classification: 15A18 15A69
متن کاملSymmetric Tensors and Symmetric Tensor Rank
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors. Any symmetric tensor can be decomposed into a linear combination of rank-1 tensors, each of them being symmet...
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Well known connections exist between the singular value decomposition of a matrix A and the Schur decomposition of its symmetric embedding sym(A) = ([ 0A ; A 0 ]). In particular, if σ is a singular value of A then +σ and −σ are eigenvalues of the symmetric embedding. The top and bottom halves of sym(A)’s eigenvectors are singular vectors for A. Power methods applied to A can be related to power...
متن کاملComputing symmetric rank for symmetric tensors
We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for 2 × · · · × 2 tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetric rank strata for some secant varieties of Veronese varieties.
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ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2011
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081081003621295