ABSTRACT
Sometimes it is useful to resolve a tensor along another triad of base vectors other than a single orthonormal set. The components of vectors and higher-order tensors will generally change upon rotation or reflection of base vectors. Of course, the tensors themselves remain invariant upon a change of basis. The coordinates of a fixed point will generally change both upon a rotation or reflection of base vectors and upon a change of the origin of coordinates. The spectral representation of a symmetric tensor can be obtained by a rotation and/or reflection of base vectors. A two-dimensional tensor is a tensor that may be resolved into components along only two orthonormal base vectors. A three-dimensional rotation tensor may be characterized by three Euler or orientation angles, which are successive angles of rotation about a set of mutually orthogonal axes. In a two-dimensional space, the contravariant components of the metric tensor are expressed in terms of the covariant components.
