Optimal l-one Rank One Matrix Decompositions

Radu Balan; Kasso A. Okoudjou; Michael Rawson; Yang Wang; Rui Zhang

doi:10.1007/978-3-030-61887-2

Optimal l-one Rank One Matrix Decompositions

Functional Analysis 2022-02-03 v1 Operator Algebras

Authors: Radu Balan , Kasso A. Okoudjou , Michael Rawson , Yang Wang , Rui Zhang

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Abstract

In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive semidefinite matrices we give explicitly these optimal decompositions. These classes include diagonally dominant matrices and certain of their generalizations, $2\times 2$ , and a class of $3\times 3$ matrices.

Keywords

hadamard matrices matrix rank low-rank matrix approximation

Cite

@article{arxiv.2002.00879,
  title  = {Optimal l-one Rank One Matrix Decompositions},
  author = {Radu Balan and Kasso A. Okoudjou and Michael Rawson and Yang Wang and Rui Zhang},
  journal= {arXiv preprint arXiv:2002.00879},
  year   = {2022}
}

Comments

Will appear in a Springer book "Harmonic Analysis and Applications", Ed. M. Rassias

Optimal l-one Rank One Matrix Decompositions

Abstract

Keywords

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