On a determinantal inequality arising from diffusion tensor imaging

Minghua Lin

On a determinantal inequality arising from diffusion tensor imaging

Rings and Algebras 2016-04-15 v1 Functional Analysis

Authors: Minghua Lin

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.

Keywords

determinants

Cite

@article{arxiv.1604.04141,
  title  = {On a determinantal inequality arising from diffusion tensor imaging},
  author = {Minghua Lin},
  journal= {arXiv preprint arXiv:1604.04141},
  year   = {2016}
}

Comments

I hope the reader could find a piece of interesting stuff and interesting questions in the preprint

On a determinantal inequality arising from diffusion tensor imaging

Abstract

Keywords

Cite

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