Levi-Civita symbol

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 and physics. 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