Editing Covariant transformation (section)

===Without coordinates===
A [[tensor]] of [[type of a tensor|type (''r'', ''s'')]] may be defined as a real-valued multilinear function of ''r'' dual vectors and ''s'' vectors. Since vectors and dual vectors may be defined without dependence on a coordinate system, a tensor defined in this way is independent of the choice of a coordinate system.

The notation of a tensor is
:<math>\begin{align}
            &T\left(\sigma, \ldots ,\rho, \mathbf{u}, \ldots, \mathbf{v}\right) \\
  \equiv {} &{T^{\sigma \ldots \rho}}_{\mathbf{u} \ldots \mathbf{v}}
\end{align}</math>
for dual vectors (differential forms) ''ρ'', ''σ'' and tangent vectors <math>\mathbf{u}, \mathbf{v}</math>. In the second notation the distinction between vectors and  differential forms is more obvious.