Some generalizations of the DDVV and BW inequalities

Ge, Jianquan; Li, FaGui; Zhou, Yi

doi:10.48550/arxiv.1807.07307

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The Equality Holds If and Only If |X1

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2020

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“…complex symmetric) matrices (cf. [5], [18]), we can also expect for the same conjectures as above with all matrices being complex matrices 1 . In fact we will prove the relations of Theorem 1.1 between these conjectures in complex version.…”

Section: Introductionsupporting

confidence: 69%

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On some conjectures by Lu and Wenzel

et al. 2020

Linear Algebra and its Applications

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In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward several new conjectures which will be shown equivalent to Conjecture 2. In particular, we prove Conjecture 2 and hence all conjectures in some special cases. For Conjecture 3, we obtain a bigger upper bound 2 + √ 10/2, and we also give a weaker answer for the more general Question 1. In addition, we obtain some new simple proofs of the complex BW inequality and the condition for equality.2010 Mathematics Subject Classification. 15A45, 15B57, 53C42.

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Section: Introductionsupporting

confidence: 69%

“…We remind that for general Hermitian matrices the optimal constant c = 4 3 is bigger than 1 here (cf. Section 1, [17], [18]).…”

Section: The Equality Holds If and Only If |Xmentioning

confidence: 99%