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

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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