The Levi-Civita symbol
, also called the permutation symbol
, is defined as follows:
It is named after Tullio Levi-Civita. It is used in many areas of mathematics
. For example, in linear algebra
, the cross product
of two vectorss
can be written as:
or more simply:
This can be further simplified by using Einstein notation
The tensor whose components are given by the Levi-Civita symbol (a tensor of covariant rank 3) is sometimes called the permutation tensor.
The Levi-Civita symbol can be generalized to higher dimensions:
See even permutation
or symmetric group
for a definition of 'even permutation' and 'odd permutation'
A related symbol is the Kronecker delta.\n