Distance Optimization in the Grassmannian of Lines
Algebraic Geometry
2026-02-02 v1 Optimization and Control
Abstract
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, and the squaring operation takes Pl\"ucker coordinates to projection coordinates. We develop metric algebraic geometry for varieties of lines in this linear algebra setting. The Grassmann distance (GD) degree is introduced as a new invariant for subvarieties of a Grassmannian. We study the GD degree for Schubert varieties and other models.
Keywords
Cite
@article{arxiv.2601.22843,
title = {Distance Optimization in the Grassmannian of Lines},
author = {Hannah Friedman and Andrea Rosana and Bernd Sturmfels},
journal= {arXiv preprint arXiv:2601.22843},
year = {2026}
}
Comments
21 pages, 1 figure