Some matrix inequalities of log-majorization type
Bo-Yan Xi, Fuzhen Zhang
TL;DR
This paper introduces new matrix inequalities based on log-majorization for eigenvalues and applies them to enhance the Hua-Marcus inequalities, resulting in stronger, more general results.
Contribution
The paper presents novel matrix inequalities of log-majorization type and generalizes existing Hua-Marcus inequalities with improved strength and scope.
Findings
New matrix inequalities of log-majorization type for eigenvalues
Generalization and strengthening of Hua-Marcus inequalities
Results are more comprehensive than previous inequalities
Abstract
The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua-Marcus' inequalities. Our results are stronger and more general than the existing ones.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMatrix Theory and Algorithms · Mathematical Inequalities and Applications · Graph theory and applications