Contravariant tensor ($T^{\prime \mu \nu }={\Lambda }^{\mu }{}_{\alpha }{\Lambda }^{\nu }{}_{\beta }{T}^{\alpha \beta }$)

A contravariant tensor transforms with one forward coordinate Jacobian for each upper index. A Lorentz four-vector is the rank-one example; the electromagnetic field tensor with two upper indices is a rank-two example. Lower-index covariant tensors transform with inverse Jacobians, and full contractions yield scalars. Index position specifies a transformation law rather than implying that the numerical components are invariant.