Classifying Linear Matrix Inequalities via Abstract Operator Systems
Functional Analysis
2023-01-27 v1 Algebraic Geometry
Operator Algebras
Abstract
We systematically study how properties of abstract operator systems help classifying linear matrix inequality definitions of sets. Our main focus is on polyhedral cones, the 3-dimensional Lorentz cone, where we can completely describe all defining linear matrix inequalities, and on the cone of positive semidefinite matrices. Here we use results on isometries between matrix algebras to describe linear matrix inequality definitions of relatively small size. We conversely use the theory of operator systems to characterize special such isometries.
Keywords
Cite
@article{arxiv.2301.11054,
title = {Classifying Linear Matrix Inequalities via Abstract Operator Systems},
author = {Martin Berger and Tom Drescher and Tim Netzer},
journal= {arXiv preprint arXiv:2301.11054},
year = {2023}
}