Some generalizations of the DDVV and BW inequalities
| Autor: | Yi Zhou, Fagui Li, Jianquan Ge |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Commutator Pure mathematics Inequality Applied Mathematics General Mathematics media_common.quotation_subject 010102 general mathematics Clifford algebra Skew Mathematics - Operator Algebras Erdős–Mordell inequality 01 natural sciences Linear subspace Hermitian matrix Differential Geometry (math.DG) FOS: Mathematics Mathematics::Differential Geometry 0101 mathematics Operator Algebras (math.OA) 15A45 15B57 53C42 Mathematics media_common |
| Popis: | 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. Comment: 21 pages, accepted by Transactions of the American Mathematical Society |
| Databáze: | OpenAIRE |
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