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arXiv · 1502.06902

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

Koenraad M. R. Audenaert
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Abstract

We prove that for positive semidefinite matrices $A$ and $B$ the following determinantal inequality holds: \[ \det(I+A\#B)\le \det(I+A^{1/2}B^{1/2}), \] where $A\#B$ is the geometric mean of $A$ and $B$. We apply this inequality to the study of interpolation methods in diffusion tensor imaging.

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Koenraad M. R. Audenaert. 2015-02-18. A Determinantal Inequality for the Geometric Mean with an Application in Diffusion Tensor Imaging. https://arxiv.org/abs/1502.06902

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