Tensor
Tensors are mathematical objects consisting of indices and components, which obey rules of transformation. Tensor analysis is useful in mechanical engineering, electromagnetic theory, differential geometry, and the general theory of relativity.
Vectors and matrices are examples of more general objects called tensors. Tensors are defined via their transformation properties: suppose we have a set of numbers 
, and we want to know how their values change under rotation of Cartesian axes. If the values in the new co-ordinate system 
can be written
where 
are the elements of a rotation matrix then the are said to be the components of a rank one tensor. Similarly, the components of a rank two tensor satisfy
and for higher order tensors, we just keep adding more of the rotation matrices. Scalars, vectors and matrices are rank zero, rank one and rank two tensors respectively.
