tensor,
n. a multilinear differential form invariant with respect to a group of permissible coordinate transformations in n-space; an element of a tensor product. A tensor of type (r, s) is a member of the product
of the vector space T with itself r times and with its dual, T*, s times, and has r superscripts and s subscripts. Different bases (see base) of T lead to different bases of T*, and hence to different bases for the tensors; however, a component transformation law exists. If we chose the basis of T to be orthonormal we obtain Cartesian tensors. A zero-order tensor is a scalar, and has no superscript or subscript. A first-order tensor is a member of T or T* (according as it is covariant or contravariant), and corresponds to a vector; it has one subscript or superscript. A second-order tensor can be represented by a matrix, and has a total of two subscripts and superscripts, that is, it is a member of T2, T2, or T11.