LeviCivita symbol
The
LeviCivita symbol, also called the
permutation symbol, is defined as follows:
It is named after Tullio LeviCivita. 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 LeviCivita symbol (a tensor of covariant rank 3) is sometimes called the permutation tensor.
The LeviCivita 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