Kronecker Delta

The Kronecker delta, named for Leopold Kronecker, is a function of two variables, usually non-negative integers i and j, that equals 1 when the variables are equal and 0 otherwise. It appears throughout mathematics, physics, engineering and computer science as a compact way of writing this definition, and generalized versions of it are used in differential geometry and tensor calculus, including in formulations of gauge theory. In linear algebra the entries of the n by n identity matrix are exactly the values of the Kronecker delta, and the inner product of two vectors written as n-tuples can be expressed as a sum over the Kronecker delta, which picks out only the matching-index terms; i and j are commonly restricted to a set such as 1 through n, but the Kronecker delta can be defined on any set.