Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911186466897920 |
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| author | Friedman, Hannah Hoşten, Serkan |
| author_facet | Friedman, Hannah Hoşten, Serkan |
| contents | Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure of the algebraic complexity is the amount of complex critical points of the corresponding optimization problem. After an exposition of different realizations of these manifolds as algebraic varieties we present a sample of optimization problems over them and we compute their algebraic complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective Friedman, Hannah Hoşten, Serkan Optimization and Control Algebraic Geometry Statistics Theory Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure of the algebraic complexity is the amount of complex critical points of the corresponding optimization problem. After an exposition of different realizations of these manifolds as algebraic varieties we present a sample of optimization problems over them and we compute their algebraic complexity. |
| title | Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective |
| topic | Optimization and Control Algebraic Geometry Statistics Theory |
| url | https://arxiv.org/abs/2505.15969 |