# 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 ${\delta}_{j}^{i}$. 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 |
---|---|

Canonical name | KroneckerDelta |

Date of creation | 2013-03-22 12:06:23 |

Last modified on | 2013-03-22 12:06:23 |

Owner | akrowne (2) |

Last modified by | akrowne (2) |

Numerical id | 7 |

Author | akrowne (2) |

Entry type | Definition |

Classification | msc 15A99 |

Related topic | IdentityMatrix |

Related topic | LeviCivitaPermutationSymbol3 |