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)

(1)

for which

(2)

Now let ,
then any set of quantities which transform according to

(3)

or, defining

(4)

according to

(5)

is a contravariant tensor. Contravariant tensors are indicated with raised indices, i.e., .

for ,
2, 3, meaning that contravariant and covariant tensors are equivalent. Such tensors
are known as Cartesian tensor. The two types
of tensors do differ in higher dimensions, however.