What are the tensors define variant and covariant tensor?

A covariant tensor, denoted with a lowered index (e.g., ) is a tensor having specific transformation properties. In general, these transformation properties differ from those of a contravariant tensor.

In which coordinate system there is no difference between contravariant and covariant tensors?

For orthogonal transformations and rectangular Cartesian coordinates, there is no distinction between covariant and contravariant components.

What are Contravariant tensors?

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)

What are contravariant and covariant four vector?

A contravariant 4-vector is a set of 4 quantities which transform under a Lorentz transformation like (ct,r) = (x0,x1,x2,x3). A covariant 4-vector is a set of 4 quantities which transform under a Lorentz transformation like (ct,-r) = (x0,x1,x2,x3).

What is the difference between covariant and contravariant vectors?

In differential geometry, the components of a vector relative to a basis of the tangent bundle are covariant if they change with the same linear transformation as a change of basis. They are contravariant if they change by the inverse transformation.

What does contravariant mean?

contravariant (not comparable) (category theory, of a functor) which reverses composition. (object-oriented programming) Using or relating to contravariance.

What does covariant mean?

Covariant(noun) a function involving the coefficients and the variables of a quantic, and such that when the quantic is lineally transformed the same function of the new variables and coefficients shall be equal to the old function multiplied by a factor.

What is the difference between contravariant?

As nouns the difference between contravariance and contravariant. is that contravariance is ( label) the reversal of the order of data types acted upon by an operator while contravariant is a bihomogeneous polynomial in dual variables of x”, ”y”, and the coefficients of some homogeneous form in ”x”, ”y , that is invariant under some group of linear transformations.

Is there a contravariant derivative?

The covariant derivative is a generalization of the directional derivative from vector calculus. As with the directional derivative, the covariant derivative is a rule, , which takes as its inputs: (1) a vector, u, defined at a point P, and (2) a vector field, v, defined in a neighborhood of P.