PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{bourin2026matrix,
title = {{Matrix Triangle Inequalities: Past, Present, and Future}},
author = {Jean-Christophe Bourin and Teng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30538},
eprint = {2610.30538},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30538},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix Triangle Inequalities: Past, Present, and Future
AU - Jean-Christophe Bourin
AU - Teng Zhang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30538
UR - https://arxiv.org/abs/2610.30538
AB - 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.
ER -