Every day we experiment motion and shape change of continuum media, assembly of different space dimension structures, fluids, solids which exhibit numerous evolutions either particular or general: large deformations, incompressibility, cavitation, contact, surface tension, defects, dislocations,... Stretch and rotation are a common feature of these motions and phenomenons. We base a continuum mechanics predictive theory on stretch and rotation quantified by matrices. In this Chapter, the change of the frame which is used to report the motion is investigated. Among the frame changes, i.e., the motions of the frame with respect to a frame tracker, we choose those that we judge not to change the shape of the frame-structure system. They are the system rigidifying frame changes.