Kronecker deltaKroneckerDelta2002-01-04 18:20:562006-10-28 23:08:58Definition\usepackage{amssymb}
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\usepackage{xypic}The \emph{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\cite{Higham}.
{\bf 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 $I=(\delta_{ij})$.
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\bibitem{Higham} N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.
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