5 papers
Eigenvector Varieties
Sandra Di Rocco, Bernd Sturmfels, Svala Sverrisdóttir
Any linear space of square matrices has an associated eigenvector variety. Its points are eigenvectors of matrices from that linear space. We present a systematic study of eigenvec…
Gram Matrices for Isotropic Vectors
Yassine El Maazouz, Bernd Sturmfels, Svala Sverrisdóttir
We investigate determinantal varieties for symmetric matrices that have zero blocks along the main diagonal. In theoretical physics, these arise as Gram matrices for kinematic vari…
Kinematic Varieties for Massless Particles
Smita Rajan, Svala Sverrisdóttir, Bernd Sturmfels
We study algebraic varieties that encode the kinematic data for massless particles in -dimensional spacetime subject to momentum conservation. Their coordinates are spinor b…
The Two Lives of the Grassmannian
Karel Devriendt, Hannah Friedman, Bernhard Reinke +1
The real Grassmannian is both a projective variety (via Plücker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develo…
Coupled Cluster Degree of the Grassmannian
Viktoriia Borovik, Bernd Sturmfels, Svala Sverrisdóttir
We determine the number of complex solutions to a nonlinear eigenvalue problem on the Grassmannian in its Plücker embedding. This is motivated by quantum chemistry, where it repres…