generalized Kronecker delta symbol
Let and be natural numbers such that . Further, let and be natural numbers in for all in . Then the generalized Kronecker delta symbol, denoted by , is zero if or for some , or if as sets. If none of the above conditions are met, then is defined as the sign of the permutation that maps to .
From the definition, it follows that when , the generalized Kronecker delta symbol reduces to the traditional delta symbol . Also, for , we obtain
where is the Levi-Civita permutation symbol.
The first equality follows since the sum one the first line has only one non-zero term; the term for which . The second equality follows from the definition of the determinant.
|Title||generalized Kronecker delta symbol|
|Date of creation||2013-03-22 13:31:38|
|Last modified on||2013-03-22 13:31:38|
|Last modified by||matte (1858)|