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.
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}
}
Comments
15 pages