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Some generalizations of the DDVV and BW inequalities

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arxiv 1807.07307 v2 pith:XF442CE4 submitted 2018-07-19 math.DG math.OA

Jianquan Ge , FaGui Li , Yi Zhou This is my paper · ORCID
classification math.DGmath.OA
keywords matricesinequalitiescliffordcomplexddvv-typegeneralizeinequalityquaternionic
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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.

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  1. On some conjectures by Lu and Wenzel

    math.DG 2019-08 reject novelty 6.0 of 10

    The complex Lu-Wenzel commutator conjecture is proven for normal, rank-one, and 2x2/3x3 matrices, but the proof of the unifying equivalence contains a gap.

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