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

Koenraad M. R. Audenaert

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 geometr…