Tensor
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 <math>v_i</math>, and we want to know how their values change under rotation of Cartesian axes. If the values in the new co-ordinate system <math>v'_i</math> can be written
<math> v'_i=L_{ij}v_j </math>
where <math>L_{ij}</math> are the elements of a rotation matrix then the <math>v_i</math> are said to be the components of a rank one tensor. Similarly, the components of a rank two tensor satisfy
<math> a'_{ij}=L_{im}L_{jn}a_{mn} </math>
and for higher order tensors, we just keep adding more of the <math>L_{ij}</math> rotation matrices. Scalars, vectors and matrices are rank zero, rank one and rank two tensors respectively.