Kronecker delta

English

Noun

1. Template:Lb A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
   • Template:Quote-book
   • 2007, J. N. Reddy, An Introduction to Continuum Mechanics, Template:W, page 20,

     Further, the Kronecker delta and the permutation symbol are related by the identity, known as the $e$-$\delta$ identity [see Problem 2.5(d)],

     $e_{ijk}{e}_{imn}={\delta }_{jm}{\delta }_{kn}-{\delta }_{jn}{\delta }_{km}$.      (2.2.43)

     The permutation symbol and the Kronecker delta prove to be very useful in proving vector identities.

   • Template:Quote-book
2. Template:Lb A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.

Usage notes

• The notation ${\delta }^{ij}$ and ${\delta }_j^i$ are also sometimes used.
• In linear algebra, the Kronecker delta can be regarded as a tensor of type (1,1).
• The function can also be expressed using Iverson bracket notation, as $[i=j]$.
• The single-argument function is equivalent to setting $j=0$ in the binary function.

Synonyms

• Template:Sense Template:L, Template:L

Derived terms

• Template:L

Translations

• Chinese:

  Mandarin: Template:T

See also

• Template:L
• Template:L
• Template:L
• Template:L
• Template:L
• Template:L
• Template:L

Further reading

• Template:Pedia
• Template:Pedia