nLab
Kronecker delta

Contents

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

Revised on May 26, 2017 12:46:28 by Urs Schreiber (92.218.150.85)