Symbols:Greek/Delta/Kronecker Delta
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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:
$\quad \forall \tuple {\alpha, \beta} \in \Gamma \times \Gamma: \delta_{\alpha \beta} := \begin{cases} 1_R & : \alpha = \beta \\ 0_R & : \alpha \ne \beta \end{cases}$
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}
.
Tensor Form
- ${\delta^i}_j$
When used in the context of tensors, the notation for the Kronecker delta can often be seen as ${\delta^i}_j$.
The $\LaTeX$ code for \({\delta^i}_j\) is {\delta^i}_j
.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Appendix $1$: Symbols and Conventions: Greek Alphabet
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Kronecker delta
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Kronecker delta
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): $\delta_{i j}$