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Euclidean Distance Optimization Within the Grassmannian
Hannah Friedman, Serkan Hoşten, Andrea Rosana
Given a subvariety of the Grassmannian and a data point, we seek to find a point on the subvariety minimizing the Euclidean distance to the data point. The number of complex critic…
Maximum Likelihood Estimation on the Grassmannian of Lines
Hannah Friedman
We study the positive Grassmannian through the lens of algebraic statistics. A closed formula is presented for the maximum likelihood degree of the Grassmannian of lines. We study…
Distance Optimization in the Grassmannian of Lines
Hannah Friedman, Andrea Rosana, Bernd Sturmfels
The square of a skew-symmetric matrix is a symmetric matrix whose eigenvalues have even multiplicities. When the matrices have rank two, they represent the Grassmannian of lines, a…
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…