  We give a geometric interpretation of the soft elastic deformation modes of
nematic elastomers, with explicit examples, for both uniaxial and biaxial
nematic order. We show the importance of body rotations in this non-classical
elasticity and how the invariance under rotations of the reference and target
states gives soft elasticity (the Golubovic and Lubensky theorem). The role of
rotations makes the Polar Decomposition Theorem vital for decomposing general
deformations into body rotations and symmetric strains. The role of the square
roots of tensors is discussed in this context and that of finding explicit
forms for soft deformations (the approach of Olmsted).
