Tensor

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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 vi, and we want to know how their values change under rotation of Cartesian axes. If the values in the new co-ordinate system v'i can be written

v'i = Lijvj

where Lij are the elements of a rotation matrix then the vi are said to be the components of a rank one tensor. Similarly, the components of a rank two tensor satisfy

a'ij = LimLjnamn

and for higher order tensors, we just keep adding more of the Lij rotation matrices. Scalars, vectors and matrices are rank zero, rank one and rank two tensors respectively.

See also

Suffix notation

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