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The Kronecker delta function (represented with δ) is a piecewise function of two variables such that

\delta_{ij} = \begin{cases} 1, & i = j \\ 
0, & i \ne j \end{cases}

It is most useful when used for integers. For example, the n × n identity matrix can be written as a matrix where each entry is the Kronecker delta of i and j. This is useful for defining an inner or dot product:

\langle u,v \rangle = \sum_{ij} \delta_{ij} u_{i} v_{j}

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