ABSTRACT
This chapter explains tensors in oblique Cartesian coordinate systems. Oblique cartesian coordinate systems are systems in which the coordinate axes are straight lines that are not necessarily perpendicular to each other. The terms covariant and contravariant have to do with the manner in which the components of the vector transform under a change of oblique coordinate systems. With slight modifications, tensors in nonrectangular cartesian coordinate systems possess much the same algebraic properties as cartesian tensors. The modifications are necessitated by the difference in the transformation laws governing covariant and contravariant components of tensors. One aspect of the algebra of cartesian tensors that needs certain modification is the operation of contraction and, as a result, the operation of inner product. In order for the contraction of two tensors to be valid, the contraction must be performed over a pair of indices, one of which must be a subscript and the other a superscript.
