What is covariant tensor?

) is a tensor having specific transformation properties. In general, these transformation properties differ from those of a contravariant tensor. Therefore, raising and lowering indices is trivial, hence covariant and contravariant tensors have the same coordinates, and can be identified. …

What do you mean by contravariant tensor?

specific transformation properties
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)

Is magnetic field a tensor?

The electric field and the magnetic field are perpendicular on each other and they form a tensor – a vector with magnitudes in two directions, called the electromagnetic tensor. , Electromagnetism is one of the frameworks of the universe.

Why is there no contravariant derivative?

But while upper indices are often used in conjunction with the covariant derivative operator for notational convenience, it is not usually called the “contravariant derivative”. That is because the actual differentiation still takes place with respect to tangent vectors, whether or not indices are raised afterwards.

Is force a contravariant?

In the language of Einstein-style index gymnastics, applied in a nonrelativistic context, this amounts to a statement that energy is a scalar, and displacement is a contravariant (upper-index) vector, so force should naturally be considered as a covariant (lower-index) vector.

What is the difference between a contravariant and a covariant tensor?

A contravariant tensor (in other words a vector), transform ‘oppositely’ (contra) to the way basis vectors transform, while a covariant tensor (or dual vector) transforms in he same way as basis vectors.

What is the difference between contravariant vectors and covariant vectors?

A contravariant vector is the name for the first type of vector, whereas a covariant vector is the name for the second type. The reason things in GR end up being covariant vectors is that with GR you are generally dealing with a field.

Is a potential energy field a covariant or contravariant vector?

In the former case, changing the units from meters to kilometers would change a 3000 meter per second vector into a 3 kilometer per second vector, making it a contravariant vector. By contrast, the gradiant of a potential energy field might be 3 ergs per meter; but it would become 3000 ergs per kilometer, making it a covariant vector.

What is the difference between higher order tensors and second-order tensors?

Higher-order tensors have multiple indices, and each one can be either contravariant or covariant: a second-order tensor could be , , , or , for example. The first would be purely contravariant; the second would be purely covariant; and the last two would be mixes of contravariance and covariance.