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
