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


">
" size=20>

 
 

Browse articles alphabetically:
#0">0 | #1">1 | #2">2 | #3">3 | #4">4 | #5">5 | #6">6 | #7">7 | #8">8 | #9">9 | #_">_ | #A">A | #B">B | #C">C | #D">D | #E">E | #F">F | #G">G | #H">H | #I">I | #J">J | #K">K | #L">L | #M">M | #N">N | #O">O | #P">P | #Q">Q | #R">R | #S">S | #T">T | #U">U | #V">V | #W">W | #X">X | #Y">Y | #Z">Z