A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, first consider a tensor of rank 1 (a vector) d r = d x_1 (x_1)^^ + d x_2 (x_2)^^ + d x_3 (x_3)^^, for which d x_i^, = (dx_i^, )/(dx_j) d x_j.

Cartesian tensor | contravariant vector | covariant tensor | four-vector | index raising | Lorentz tensor | metric tensor | mixed tensor | tensor