AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of almost all tensors) of a given shape (n, m, l) are presented. These improve previous results by A tkinson and Lloyd. For cubic shape tensors the typical rank is determined exactly: R(n, n, n) = ⌈ n3/(3n − 2) ⌉ (n ≠ 3
AbstractLet M be a matrix of order n=pq. Then the tensor rank of M is defined as the minimal possibl...
Upper bounds are given for the maximal rank of an element of the tensor product of three vector spac...
Tensor decompositions have been studied for nearly a century, but the well-known notion of tensor ra...
AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of alm...
AbstractThe typical rank (= maximal border rank) of tensors of a given size and the set of optimal b...
This master's thesis addresses numerical methods of computing the typical ranks of tensors over the ...
AbstractWe study the generic and typical ranks of 3-tensors of dimension l×m×n using results from ma...
AbstractThe border rank of a nondegenerate m×n×(mn−q) tensor over the complex field is mn−q provided...
It is shown that the maximal rank of m × n × ( m n - k ) tensors with k min {( m - 1 ) 2 /2 , ( ...
We introduce various notions of rank for a high order symmetric tensor taking values over the comple...
AbstractUpper bounds are given for the maximal rank of an element of the tensor product of three vec...
AbstractThe problem of obtaining upper bounds on the ranks of third order tensors is studied. New bo...
AbstractThe concept of tensor rank was introduced in the 20s. In the 70s, when methods of Component ...
We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order...
The tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum...
AbstractLet M be a matrix of order n=pq. Then the tensor rank of M is defined as the minimal possibl...
Upper bounds are given for the maximal rank of an element of the tensor product of three vector spac...
Tensor decompositions have been studied for nearly a century, but the well-known notion of tensor ra...
AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of alm...
AbstractThe typical rank (= maximal border rank) of tensors of a given size and the set of optimal b...
This master's thesis addresses numerical methods of computing the typical ranks of tensors over the ...
AbstractWe study the generic and typical ranks of 3-tensors of dimension l×m×n using results from ma...
AbstractThe border rank of a nondegenerate m×n×(mn−q) tensor over the complex field is mn−q provided...
It is shown that the maximal rank of m × n × ( m n - k ) tensors with k min {( m - 1 ) 2 /2 , ( ...
We introduce various notions of rank for a high order symmetric tensor taking values over the comple...
AbstractUpper bounds are given for the maximal rank of an element of the tensor product of three vec...
AbstractThe problem of obtaining upper bounds on the ranks of third order tensors is studied. New bo...
AbstractThe concept of tensor rank was introduced in the 20s. In the 70s, when methods of Component ...
We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order...
The tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum...
AbstractLet M be a matrix of order n=pq. Then the tensor rank of M is defined as the minimal possibl...
Upper bounds are given for the maximal rank of an element of the tensor product of three vector spac...
Tensor decompositions have been studied for nearly a century, but the well-known notion of tensor ra...
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