24 citations · 73 across the 28 of their papers we have counts for
10 papers · 1 filter
Decomposing tensors via rank-one approximations
Alvaro Ribot, Emil Horobet, Anna Seigal +1
Matrices can be decomposed via rank-one approximations: the best rank-one approximation is a singular vector pair, and the singular value decomposition writes a matrix as a sum of…
A Real Generalized Trisecant Trichotomy
Kristian Ranestad, Anna Seigal, Kexin Wang
The classical trisecant lemma says that a general chord of a non-degenerate space curve is not a trisecant; that is, the chord only meets the curve in two points. The generalized t…
Multilinear Hyperquiver Representations
Tommi Muller, Vidit Nanda, Anna Seigal
We count singular vector tuples of a system of tensors assigned to the edges of a directed hypergraph. To do so, we study the generalisation of quivers to directed hypergraphs. Ass…
Differential Equations for Gaussian Statistical Models with Rational Maximum Likelihood Estimator
Carlos Améndola, Lukas Gustafsson, Kathlén Kohn +2
We study multivariate Gaussian statistical models whose maximum likelihood estimator (MLE) is a rational function of the observed data. We establish a one-to-one correspondence bet…
Lower bounds on the rank and symmetric rank of real tensors
Kexin Wang, Anna Seigal
We lower bound the rank of a tensor by a linear combination of the ranks of three of its unfoldings, using Sylvester's rank inequality. In a similar way, we lower bound the symmetr…
The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices
Carlos Améndola, Lukas Gustafsson, Kathlén Kohn +2
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is,…
Ranks and Singularities of Cubic Surfaces
Anna Seigal, Eunice Sukarto
We explore the connection between the rank of a polynomial and the singularities of its vanishing locus. We first describe the singularity of generic polynomials of fixed rank. We…
Ranks and Symmetric Ranks of Cubic Surfaces
Anna Seigal
We study cubic surfaces as symmetric tensors of format . We consider the non-symmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show th…
Real Rank Two Geometry
Anna Seigal, Bernd Sturmfels
The real rank two locus of an algebraic variety is the closure of the union of all secant lines spanned by real points. We seek a semi-algebraic description of this set. Its algebr…
Eigenconfigurations of Tensors
Hirotachi Abo, Anna Seigal, Bernd Sturmfels
Square matrices represent linear self-maps of vector spaces, and their eigenpoints are the fixed points of the induced map on projective space. Likewise, polynomial self-maps of a…