DOIAbstract
AbstractThe problem of obtaining upper bounds on the ranks of third order tensors is studied. New bounds are found using matrix canonical forms and nonlinear techniques from commutative algebra
AbstractThe problem of obtaining upper bounds on the ranks of third order tensors is studied. New bounds are found using matrix canonical forms and nonlinear techniques from commutative algebra
A best rank-R approximation of an order-3 tensor or three-way array may not exist due to the fact th...
AbstractThe typical rank (= maximal border rank) of tensors of a given size and the set of optimal b...
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of t...
AbstractWe study the generic and typical ranks of 3-tensors of dimension l×m×n using results from ma...
AbstractUpper bounds are given for the maximal rank of an element of the tensor product of three vec...
Let $U$, $V$ and $W$ be finite dimensional vector spaces over the same field. The rank of a tensor $...
Upper bounds are given for the maximal rank of an element of the tensor product of three vector spac...
AbstractTensor type data are becoming important recently in various application fields. We determine...
We introduce various notions of rank for a high order symmetric tensor taking values over the comple...
AbstractLet M be a matrix of order n=pq. Then the tensor rank of M is defined as the minimal possibl...
The rank and canonical forms of a tensor are concepts that naturally generalize that of a matrix. Th...
AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of alm...
Let U, V and W be finite dimensional vector spaces over the same field. The rank of a tensor t in U?...
We address the problem of the additivity of the tensor rank. That is, for two independent tensors we...
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. ...
A best rank-R approximation of an order-3 tensor or three-way array may not exist due to the fact th...
AbstractThe typical rank (= maximal border rank) of tensors of a given size and the set of optimal b...
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of t...
AbstractWe study the generic and typical ranks of 3-tensors of dimension l×m×n using results from ma...
AbstractUpper bounds are given for the maximal rank of an element of the tensor product of three vec...
Let $U$, $V$ and $W$ be finite dimensional vector spaces over the same field. The rank of a tensor $...
Upper bounds are given for the maximal rank of an element of the tensor product of three vector spac...
AbstractTensor type data are becoming important recently in various application fields. We determine...
We introduce various notions of rank for a high order symmetric tensor taking values over the comple...
AbstractLet M be a matrix of order n=pq. Then the tensor rank of M is defined as the minimal possibl...
The rank and canonical forms of a tensor are concepts that naturally generalize that of a matrix. Th...
AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of alm...
Let U, V and W be finite dimensional vector spaces over the same field. The rank of a tensor t in U?...
We address the problem of the additivity of the tensor rank. That is, for two independent tensors we...
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. ...
A best rank-R approximation of an order-3 tensor or three-way array may not exist due to the fact th...
AbstractThe typical rank (= maximal border rank) of tensors of a given size and the set of optimal b...
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of t...
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