Matrix Triangle Inequalities: Past, Present, and Future

Abstract

This survey provides a concise overview of matrix triangle inequalities. Classical topics, such as inequalities for unitarily invariant norms, are revisited from a different perspective, with a particular emphasis on unitary orbit inequalities and various notions of matrix moduli. The exposition progresses from elementary results to much more recent developments, highlighting the evolution of the subject and its ongoing directions of research.

arXiv commentaccepted in Reviews in Mathematical Physics