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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2410.15231 |
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| _version_ | 1866929551567749120 |
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| author | Choulakian, Vartan |
| author_facet | Choulakian, Vartan |
| contents | We compare the essential properties of projections in the L2 and L1 normed spaces by two methods: Projection operators and by minimization of the distance. In Euclidean geometry the orthogonality (L2- conjugacy) plays central role; while in L1 normed space L1- conjugacy (the sign function) plays central role. Furthermore, this fact appears in the Pythagorean Theorem and its Taxicab analogue. We also compare three singular value decompositions: SVD, Taxicab SVD and L1min-SVD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projections in L2 and L1 normed spaces and SVDs Choulakian, Vartan Functional Analysis 62H25, 62H30 We compare the essential properties of projections in the L2 and L1 normed spaces by two methods: Projection operators and by minimization of the distance. In Euclidean geometry the orthogonality (L2- conjugacy) plays central role; while in L1 normed space L1- conjugacy (the sign function) plays central role. Furthermore, this fact appears in the Pythagorean Theorem and its Taxicab analogue. We also compare three singular value decompositions: SVD, Taxicab SVD and L1min-SVD. |
| title | Projections in L2 and L1 normed spaces and SVDs |
| topic | Functional Analysis 62H25, 62H30 |
| url | https://arxiv.org/abs/2410.15231 |