Principal components along quiver representations
Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation of a finite quiver. Consequently, we are able to define and...
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| Format: | Journal article |
| Language: | English |
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Springer
2022
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| _version_ | 1826311428946001920 |
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| author | Seigal, A Harrington, H Nanda, V |
| author_facet | Seigal, A Harrington, H Nanda, V |
| author_sort | Seigal, A |
| collection | OXFORD |
| description | Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation of a finite quiver. Consequently, we are able to define and compute principal components with respect to quiver representations. These principal components are solutions to constrained optimisation problems defined over the space of sections and are eigenvectors of an associated matrix pencil.
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| first_indexed | 2024-03-07T08:08:16Z |
| format | Journal article |
| id | oxford-uuid:85341ced-02a3-4afd-aab6-2eb3efba0254 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:08:16Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:85341ced-02a3-4afd-aab6-2eb3efba02542023-11-10T11:46:55ZPrincipal components along quiver representationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:85341ced-02a3-4afd-aab6-2eb3efba0254EnglishSymplectic ElementsSpringer2022Seigal, AHarrington, HNanda, VQuiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation of a finite quiver. Consequently, we are able to define and compute principal components with respect to quiver representations. These principal components are solutions to constrained optimisation problems defined over the space of sections and are eigenvectors of an associated matrix pencil. |
| spellingShingle | Seigal, A Harrington, H Nanda, V Principal components along quiver representations |
| title | Principal components along quiver representations |
| title_full | Principal components along quiver representations |
| title_fullStr | Principal components along quiver representations |
| title_full_unstemmed | Principal components along quiver representations |
| title_short | Principal components along quiver representations |
| title_sort | principal components along quiver representations |
| work_keys_str_mv | AT seigala principalcomponentsalongquiverrepresentations AT harringtonh principalcomponentsalongquiverrepresentations AT nandav principalcomponentsalongquiverrepresentations |