Ranks of tensors, secant varieties of Segre varieties and fat points

By M. Catalisano, A. V. Geramita, Alessandro Gimigliano. 2002

139 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1dbd4ee80b8349be8c923d14a560b327cc69a25c

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Citations in the corpus

The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “, [88, 91] for the computational complexity approach, [16, 90] for the biological statistical approach, [92, 22, 94, 93] for the classical algebraic geometry approach, [95, 96] for the representation theory approach, [97] for a tropical approach and [98] for a multilinear algebra approach.”
On the Expressive Power of Deep Learning: A Tensor Analysis (2015, unknown): “Alternatively, we refer the reader to [16, 10, 13, 1] for proofs of this result under different settings.”
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem (2006, unknown): “dk, the determination of the generic outer product rank is an open problem in general and a nontrivial problem even in simple cases — see [13, 14] for results over C and [72, 73] for results over R.”
Combinatorial secant varieties (2005, methodology): “As pointed out in [6], finding an s-element”
Varieties with minimal secant degree and linear systems of maximal dimension on surfaces (2004, background): “ynomial interpolation problems, rank tensor computations and canonical forms, expressions of polynomials as sums of powers and Waring type problems, algebraic statistics etc. (see, for instance, [C], [CGG], [GSS], [IK]). Going back to projective algebraic geometry, let us mention the ﬁrst basic exam”
Identifiability of parameters in latent structure models with many observed variables (2008, background): “Recent works such as [1, 7, 8] have made much progress in determining when defects occur.”
On the Concept of k‐Secant Order of a Variety (2006, unknown): “(see [5] as a general reference, [3], [10], [12], [18] and § 5 below).”