Kronecker Delta

In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker, is a function of two variables, usually integers. The function is 1 if the variables are equal, and 0 otherwise:

\delta_{ij} = \left\{\begin{matrix} 0, & \mbox{if } i \ne j \\ 1, & \mbox{if } i=j \end{matrix}\right.

where Kronecker delta δij is a piecewise function of variables and . For example, δ1 2 = 0, whereas δ3 3 = 1.

In linear algebra, the identity matrix can be written as, and the inner product of vectors can be written as \textstyle \boldsymbol{a}\cdot\boldsymbol{b} = \sum_{ij} a_{i}\delta_{ij}b_{j}.

The Kronecker delta is used in many areas of mathematics.

Read more about Kronecker Delta:  Properties, Alternate Notation, Digital Signal Processing, Properties of The Delta Function, Relationship To The Dirac Delta Function, Generalizations of The Kronecker Delta, Integral Representations, The Kronecker Comb, Kronecker Integral