Mathematical notation | Elementary special functions
Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: or with use of Iverson brackets:where the Kronecker delta δij is a piecewise function of variables i and j. For example, δ1 2 = 0, whereas δ3 3 = 1. The Kronecker delta appears naturally in many areas of mathematics, physics and engineering, as a means of compactly expressing its definition above. In linear algebra, the n × n identity matrix I has entries equal to the Kronecker delta: where i and j take the values 1, 2, ..., n, and the inner product of vectors can be written as Here the Euclidean vectors are defined as n-tuples: and and the last step is obtained by using the values of the Kronecker delta to reduce the summation over j. The restriction to positive or non-negative integers is common, but in fact, the Kronecker delta can be defined on an arbitrary set. (Wikipedia).
