Kronecker delta

9.9

A rule that gives 1 when two numbers are the same and 0 when they are different

noun
/ˈkroʊnɛkər ˈdɛltə/

Specialized

: delta de Kronecker

The Kronecker delta equals 1 when both variables are the same and 0 otherwise.

Examples

When i and j are not equal, the Kronecker delta yields zero.
The Kronecker delta is frequently used to simplify expressions in linear algebra.
In tensor notation, the Kronecker delta acts as the identity matrix.
The function Kronecker delta is essential in linear algebra.
In physics, the Kronecker delta simplifies many equations.
Mathematicians often use the Kronecker delta to express conditions in proofs.
In many equations, the Kronecker delta helps eliminate terms that do not contribute.

Surface Forms

Kronecker delta singular

Kronecker deltas plural

Morphology

Kronecker + delta

Kronecker is a proper name (a mathematician) and 'delta' is usually understood as a Greek letter or a sign of change; their combination is a conventional, technical label for a specific binary function in mathematics whose meaning (1 if indices equal, 0 otherwise) is not derivable from the parts. As a named mathematical term this is language- and discipline-specific, so a B1 learner who only knows the constituents would not be able to infer the MWE's meaning.

Etymology

The term Kronecker delta is named after the mathematician Leopold Kronecker and works like a simple on/off rule. It gives 1 when two numbers are the same and 0 when they are different, so it acts like a tiny switch that says 'yes' for equal items and 'no' for unequal ones.