## ABSTRACT

This paper derives a general representation of several kinematical identities based on the eigenvalue bases theorem. Three eigenvalue bases are constructed from the eigenvectors of the left stretch tensor. The relationships between the left stretch tensor and the corresponding eigenvalue bases are established by considering the spectral representation of the left stretch tensor. The eigenvalue bases are explicitly expressed in the general coordinate-independent forms in terms of the left stretch tensor. With the general invariant representations of the eigenvalue bases, explicit relationships are obtained between several spin tensors, the material spin tensor, the deformation rate tensor, the left/right stretch tensor, the material time derivative of the strain measures and the stress conjugate to the strain measures. In addition, this paper gives simple representations of the related physical quantities, which are explicitly expressed in terms of the three coordinate-invariants of the left stretch tensor.