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.