Add to ORKGIt is shown that if V ⊆ F p n ×⋯×np is a subspace of d-tensors with dimension at least tnd-1, then there is a subspace W ⊆ V of dimension at least t/(dr)−1 p is a subspace of d-tensors with dimension whose nonzero elements all have analytic rank Ωd,p(r). As an application, we generalize a result of Altman on Szemerédi's theorem with random differences
Let νd : Pr → PN, denote the degree d Veronese embedding of Pr. For any P ∈ PN, the symmetric tensor...
Multidimensional data, or tensors, arise natura lly in data analysis applications. Hitchcock&##39;s ...
Abstract. Let K be a field and let V be a vector space of finite dimension n over K. We investigate ...
It is shown that if V ⊆ F p n ×⋯×np is a subspace of d-tensors with di...
Let U, V be two vector spaces of dimensions n and m, respectively, over an algebraically closed fiel...
Let $U$, $V$ and $W$ be finite dimensional vector spaces over the same field. The rank of a tensor $...
\u3cp\u3eGiven a tensor f in a Euclidean tensor space, we are interested in the critical points of t...
AbstractIf M is a subspace of a tensor product of vector spaces, A ⊕ B, we define r(M) = inf rank x(...
Given a tensor f in a Euclidean tensor space, we are interested in the critical points of the distan...
If r > 1 is an integer then U(r) denotes the vector space of r-fold symmetric tensors and Pr[U] is t...
Joint work with Jan Draisma and Giorgio Ottaviani. Given a tensor f in a Euclidean tensor space, we ...
AbstractLet K be a field and let Mm×n(K) denote the space of m×n matrices over K. We investigate pro...
Motivated by a problem in computational complexity, we consider the behavior of rank functions for t...
Given a random subspace H_n chosen uniformly in a tensor product of Hilbert spaces V_n ⊗ W , we cons...
International audienceWe show that for a nonnegative tensor, a best nonnegative rank-$r$ approximati...
Let νd : Pr → PN, denote the degree d Veronese embedding of Pr. For any P ∈ PN, the symmetric tensor...
Multidimensional data, or tensors, arise natura lly in data analysis applications. Hitchcock&##39;s ...
Abstract. Let K be a field and let V be a vector space of finite dimension n over K. We investigate ...
It is shown that if V ⊆ F p n ×⋯×np is a subspace of d-tensors with di...
Let U, V be two vector spaces of dimensions n and m, respectively, over an algebraically closed fiel...
Let $U$, $V$ and $W$ be finite dimensional vector spaces over the same field. The rank of a tensor $...
\u3cp\u3eGiven a tensor f in a Euclidean tensor space, we are interested in the critical points of t...
AbstractIf M is a subspace of a tensor product of vector spaces, A ⊕ B, we define r(M) = inf rank x(...
Given a tensor f in a Euclidean tensor space, we are interested in the critical points of the distan...
If r > 1 is an integer then U(r) denotes the vector space of r-fold symmetric tensors and Pr[U] is t...
Joint work with Jan Draisma and Giorgio Ottaviani. Given a tensor f in a Euclidean tensor space, we ...
AbstractLet K be a field and let Mm×n(K) denote the space of m×n matrices over K. We investigate pro...
Motivated by a problem in computational complexity, we consider the behavior of rank functions for t...
Given a random subspace H_n chosen uniformly in a tensor product of Hilbert spaces V_n ⊗ W , we cons...
International audienceWe show that for a nonnegative tensor, a best nonnegative rank-$r$ approximati...
Let νd : Pr → PN, denote the degree d Veronese embedding of Pr. For any P ∈ PN, the symmetric tensor...
Multidimensional data, or tensors, arise natura lly in data analysis applications. Hitchcock&##39;s ...
Abstract. Let K be a field and let V be a vector space of finite dimension n over K. We investigate ...