What are the conditions for a general linear operator (e.g. matrix) to be representable as a versor sandwich product? Basically I’m thinking about something like the post Generating a 4x4 Transformation Matrix from PGA3D but in reverse.

It seems there are clear examples for orthogonal and (IIRC) skew-symmetic matrices, but is there a general test? (Full rank, positive definite, something like that?)