# Kronecker delta

The Kronecker delta $\delta_{ij}$ is defined as having value 1 when $i=j$ and 0 otherwise ($i$ and $j$ are integers). It may also be written as $\delta^{ij}$ or $\delta^{i}_{j}$. It is a special case of the generalized Kronecker delta symbol.

The delta symbol was first used in print by Kronecker in 1868[1].

Example.

The $n\times n$ identity matrix $I$ can be written in terms of the Kronecker delta as simply the matrix of the delta, $I_{ij}=\delta_{ij}$, or simply $I=(\delta_{ij})$.

## References

• 1 N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.
Title Kronecker delta KroneckerDelta 2013-03-22 12:06:23 2013-03-22 12:06:23 akrowne (2) akrowne (2) 7 akrowne (2) Definition msc 15A99 IdentityMatrix LeviCivitaPermutationSymbol3