Some generalizations of the DDVV and BW inequalities
Differential Geometry
2020-11-30 v2 Operator Algebras
Abstract
In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erd\H{o}s-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system or a Clifford algebra. We also generalize the B\"{o}ttcher-Wenzel inequality to quaternionic matrices.
Keywords
Cite
@article{arxiv.1807.07307,
title = {Some generalizations of the DDVV and BW inequalities},
author = {Jianquan Ge and FaGui Li and Yi Zhou},
journal= {arXiv preprint arXiv:1807.07307},
year = {2020}
}
Comments
21 pages, accepted by Transactions of the American Mathematical Society