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Built-in Mathematica Symbol

KroneckerDelta

KroneckerDelta[n₁, n₂, ...]
gives the Kronecker delta

, equal to 1 if all the

are equal, and 0 otherwise.

Construct an identity matrix:

Use in sums to pick out elements:

Construct an identity matrix:

Out[1]//MatrixForm=

Use in sums to pick out elements:

One-argument form:

Multi-argument form:

Arguments can be approximate numbers:

Use in sums to pick out terms:

Generate a banded matrix with two superdiagonals:

Pick out elements:

Reduce an equation containing KroneckerDelta:

The support of KroneckerDelta has measure zero:

KroneckerDelta can stay unevaluated for numeric arguments:

A larger setting for $MaxExtraPrecision can be needed:

Equality testing of the arguments takes numerical precision into account:

Express products of signatures as sums of products of Kronecker deltas:

Special cases for 3D; summation over repeated indices is assumed: