# Geometric mean of affine matrices

Hi,

I'd like to compute the geometric mean of several affine transformations (e.g. represented by 4x4 affine matrices). Going a step back, what's the geometric mean of n 3x3 matrices (with det > 0, basically representing rotations,scaling, shearing but no flips or projections).

I have seen many definitions for pos def. matrices and some work on SO(3) but not for linear or affine transforms.

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Going another step back, what does "geometric mean" mean for matrices? –  Igor Rivin Apr 3 '12 at 2:00
Do these matrices live in a nice differentiable manifold? –  Suvrit Apr 5 '12 at 20:15