  A crucial building block of the ghost free massive gravity is the square root
function of a matrix. This is a problematic entity from the viewpoint of
existence and uniqueness properties. We accurately describe the freedom of
choosing a square root of a (non-degenerate) matrix. It has discrete and (in
special cases) continuous parts. When continuous freedom is present, the usual
perturbation theory in terms of matrices can be critically ill defined for some
choices of the square root. We consider the new formulation of massive and
bimetric gravity which deals directly with eigenvalues (in disguise of
elementary symmetric polynomials) instead of matrices. It allows for a
meaningful discussion of perturbation theory in such cases, even though certain
non-analytic features arise.
