On uniqueness, existence and objectivity of S-R decomposition theorem

For a physically possible deformation field of a continuum, the deformationgradient function F can be decomposed into direct sum of a symmetric tensor S andan orthogonal tensor R. which is called S-R decomposition theorem. In this paper,the S-R decomposition unique existence theorem is proved. by employing matrix andtensor method. Also, a brief proof of its objectivity is given.