Distance Optimization in the Grassmannian of Lines
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912862687985664 |
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| author | Friedman, Hannah Rosana, Andrea Sturmfels, Bernd |
| author_facet | Friedman, Hannah Rosana, Andrea Sturmfels, Bernd |
| contents | 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 Plücker 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22843 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distance Optimization in the Grassmannian of Lines Friedman, Hannah Rosana, Andrea Sturmfels, Bernd Algebraic Geometry Optimization and Control 14M15, 15B57, 90C23 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 Plücker 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. |
| title | Distance Optimization in the Grassmannian of Lines |
| topic | Algebraic Geometry Optimization and Control 14M15, 15B57, 90C23 |
| url | https://arxiv.org/abs/2601.22843 |