Symbols:Greek/Delta/Kronecker Delta

Kronecker Delta

$\delta_{x y}$

Let $\Gamma$ be a set.

Let $R$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Then $\delta_{\alpha \beta}: \Gamma \times \Gamma \to R$ is the mapping on the cartesian square of $\Gamma$ defined as:

$\forall \tuple {\alpha, \beta} \in \Gamma \times \Gamma: \delta_{\alpha \beta} :=

\begin{cases} 1_R & : \alpha = \beta \\ 0_R & : \alpha \ne \beta \end{cases}$

This use of $\delta$ is known as the Kronecker delta notation or Kronecker delta convention.

The $\LaTeX$ code for \(\delta_{x y}\) is \delta_{x y} .

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Appendix $1$: Symbols and Conventions: Greek Alphabet
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): $\delta_{i j}$