All this GA stuff is OK but what is the problem with matrices of affine transformations?
- no closed form exponential/logarithm (i.e. cant interpolate)
- no numerical stability for subgroups (i.e. need Gramm-Shmidt, SVD)
- no covariant transformations (i.e. need adjugate to transform axial vectors)
- no geometric construction. (e.g. in GA product of two elements is (square of) versor between them)
- costly inverses (just some sign swaps in GA)
All this GA stuff is OK but what is the problem with matrices of affine transformations?