Generalized Diagonals in Positive Semi-Definite Matrices
Robert Angarone, Daniel Soskin
TL;DR
This paper characterizes all inequalities among generalized diagonals in positive semi-definite matrices, revealing they are governed by a simple partial order, extending known results from totally nonnegative matrices.
Contribution
It provides a complete description of inequalities among generalized diagonals in positive semi-definite matrices, linking them to a partial order on the symmetric group.
Findings
All inequalities among generalized diagonals are characterized by a simple partial order.
The results extend previous work on totally nonnegative matrices.
Provides a unified framework for inequalities in positive semi-definite matrices.
Abstract
We describe all inequalities among generalized diagonals in positive semi-definite matrices. These turn out to be governed by a simple partial order on the symmetric group. This provides an analogue of results of Drake, Gerrish, and Skandera on inequalities among generalized diagonals in totally nonnegative matrices.
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 · Advanced Mathematical Theories and Applications · Advanced Algebra and Logic