Matrix Completion and Decomposition in Phase Bounded Cones
Abstract
The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This paper considers the completion and decomposition problems in a broader class of cones, namely phase-bounded cones. We show that most of the main results from the PSD case carry over to the phase-bounded case. More precisely, this is done by first unveiling a duality between the completion and decomposition problems, using a dual cone interpretation. Based on this, we then derive necessary and sufficient conditions for the phase-bounded completion and decomposition problems, and also characterize all phase-bounded completions of a completable partial matrix with a banded pattern.
Cite
@article{arxiv.2409.10282,
title = {Matrix Completion and Decomposition in Phase Bounded Cones},
author = {Ding Zhang and Axel Ringh and Li Qiu},
journal= {arXiv preprint arXiv:2409.10282},
year = {2025}
}