# Dictionary:Kronecker delta (δij)

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(krō’ nek ∂r del’ t∂) In the mathematics of discrete systems,

${\displaystyle \delta _{ij}={\begin{cases}1&{\text{if }}i=j\\0&{\text{if }}i\neq j\end{cases}}}$

It has the property ${\displaystyle \sum \delta _{ij}f_{j}=f_{i}}$. Sometimes specified as the matrix

${\displaystyle \delta _{ijkl}=I={\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}}.}$

Analogous to the Dirac delta function (or impulse, q.v.) in the mathematics of continuous systems. Named for Leopold Kronecker (1823–1891), German mathematician.