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We prove that for positive semidefinite matrices $A$ and $B$ the followingdeterminantal 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 tothe study of interpolation methods in diffusion tensor imaging.

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