Optimal ℓ1 Rank One Matrix Decomposition

Radu Balan, Kasso Okoudjou, Michael G. Rawson, Yang Wang, rui zhang

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 × 2, and a class of 3 × 3 matrices.