205 citations · 676 across the 36 of their papers we have counts for
6 papers · 1 filter
Grassmann secants, identifiability, and linear systems of tensors
Edoardo Ballico, Alessandra Bernardi, Maria Virginia Catalisano +1
For any irreducible non-degenerate variety , we give a criterion for the -identifiability of . If , then the -identifiability…
On the cactus rank of cubics forms
Alessandra Bernardi, Kristian Ranestad
We prove that the smallest degree of an apolar 0-dimensional scheme of a general cubic form in variables is at most , when , and therefore smaller than the ran…
Algebraic Geometry tools for the study of entanglement: an application to spin squeezed states
Alessandra Bernardi, Iacopo Carusotto
A short review of Algebraic Geometry tools for the decomposition of tensors and polynomials is given from the point of view of applications to quantum and atomic physics. Examples…
General Tensor Decomposition, Moment Matrices and Applications
Alessandra Bernardi, Jerome Brachat, Pierre Comon +1
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous t…
Higher secant varieties of embedded in bi-degree
Edoardo Ballico, Alessandra Bernardi, Maria Virginia Catalisano
In this paper we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of via the section of the sheaf $\mathca…
Symmetric tensor rank with a tangent vector: a generic uniqueness theorem
Edoardo Ballico, Alessandra Bernardi
Let , , be the order Veronese embedding of . Let , be the tangent developabl…