منابع مشابه
Successive Rank-One Approximations for Nearly Orthogonally Decomposable Symmetric Tensors
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing inspiration from the matrix case, the successive rank-one approximations (SROA) scheme has been proposed and shown to yield this tensor decomposition exactly, an...
متن کاملSuccessive Rank-One Approximations of Nearly Orthogonally Decomposable Symmetric Tensors
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing inspiration from the matrix case, the successive rank-one approximations (SROA) scheme has been proposed and shown to yield this tensor decomposition exactly, an...
متن کاملDecomposable symmetric designs
The first infinite families of symmetric designswere obtained fromfinite projective geometries, Hadamardmatrices, and difference sets. In this paper we describe two general methods of constructing symmetric designs that give rise to the parameters of all other known infinite families of symmetric designs. The method of global decomposition produces an incidence matrix of a symmetric design as a...
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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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1970
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1970.35.65