On a determinantal inequality arising from diffusion tensor imaging

Abstract

In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality $$\det (A^2+|BA|)\le \det (A^2+AB),$$ where $A,B$ are $n\times n$ positive semidefinite matrices. We complement his result by proving $$\det (A^2+|AB|)\ge \det (A^2+AB).$$ Our proofs feature the fruitful interplay between determinantal inequalities and majorization relations. Some related questions are mentioned.

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References in corpus (1)

• A Determinantal Inequality for the Geometric Mean with an Application in Diffusion Tensor Imaging