On a determinantal inequality arising from diffusion tensor imaging

2016/04/08 by Lin, Minghua
#FOS: Mathematics #Functional Analysis (math.FA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1604.04141

Abstract

In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality det(A²+|BA|)≤ det(A²+AB), where A, B are n× n positive semidefinite matrices. We complement his result by proving det(A²+|AB|)≥ det(A²+AB). Our proofs feature the fruitful interplay between determinantal inequalities and majorization relations. Some related questions are mentioned.

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