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 vectors 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.
Referenced By
Einstein convention | Einstein notation | Einstein summation | Einstein summation convention | Einstein summation notation | Epsilon | Epsilon (letter) | Glossary of tensor theory | Kronecker delta | List of mathematical topics (J-L) | Multilinear algebra | Pauli matrices | Pauli matrix | Tensor notation
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