In the tensor space SymdR2 of binary forms we study the best rank k approximation problem. The critical points of the best rank 1 approximation problem are the eigenvectors and it is known that they span a hyperplane. ...

Given a tensor f in a Euclidean tensor space, we are interested in the critical points of the distance function from f to the set of tensors of rank at most k, which we call the critical rank-at-most-k tensors for f. When ...

We characterize directs sums of twists of symmetric powers of the universal quotient bundle over the Grassmannian of lines. We use a method that could be used for analogue results on any arbitrary variety, and that should ...

In this article, we introduce a relation including ideals of an evo-lution algebra and hereditary subsets of vertices of its associated graph andestablish some properties among them. This relation allows us to determinemaximal ...

This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, Zariski topology and the ...

The starting point of this work is the fact that the class of evolution algebras over a fixed field is closed under tensor product. We prove that, under certain conditions, the tensor product is an evolution algebra if and ...

We recall the notion of hyperdeterminant of a multidimensional matrix (tensor). We prove that if we restrict the hyperdeterminant to a skew-symmetric tensor p V ⊆ V ⊗p with p ≥ 3 then it vanishes. The hyperdeterminant ...

Nowadays one of the main focuses of the Spanish University system is achieving the active learning paradigm in the context of its integration into the European Higher Education Area. This goal is being addressed by means ...