The simplest interpretation of the Kronecker delta is as the discrete version of the Delta Function defined by

(1) 
It has the Complex Generating Function

(2) 
where and are Integers. In 3space, the Kronecker delta satisfies the identities

(3) 

(4) 

(5) 

(6) 
where Einstein Summation is implicitly assumed, , and is the Permutation Symbol.
Technically, the Kronecker delta is a Tensor defined by the relationship

(7) 
Since, by definition, the coordinates and are independent for ,

(8) 
so

(9) 
and is really a mixed second Rank Tensor. It satisfies

(10) 

(11) 

(12) 
See also Delta Function, Permutation Symbol
© 19969 Eric W. Weisstein
19990526