nLab Kronecker delta

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Definition

For II a set, the Kronecker delta-function is the function I×I{0,1}I \times I \to \{0,1\} which takes the value 0 everywhere except on the diagonal, where it takes the value 1.

Often one writes for elements i,jIi,j \in I

δ j iδ(i,j). \delta^{i}_j \coloneqq \delta(i,j) \,.

Then

δ j i={1 ifi=j 0 otherwise \delta^i_j = \left\{ \array{ 1 & if i = j \\ 0 & otherwise } \right.

In constructive mathematics, it is necessary that II have decidable equality; alternatively, one could let the Kronecker delta take values in the lower reals.

Generalizations

References

Named after Leopold Kronecker.

See also

Last revised on April 27, 2024 at 10:42:29. See the history of this page for a list of all contributions to it.