English

Projections in L2 and L1 normed spaces and SVDs

Functional Analysis 2024-10-22 v1

Abstract

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.

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Cite

@article{arxiv.2410.15231,
  title  = {Projections in L2 and L1 normed spaces and SVDs},
  author = {Vartan Choulakian},
  journal= {arXiv preprint arXiv:2410.15231},
  year   = {2024}
}

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15 pages