Kronecker delta

== English == === Etymology === Named after German mathematician Leopold Kronecker (1823–1891) === Noun === Kronecker delta (plural Kronecker deltas) (mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise. 2007, J. N. Reddy, An Introduction to Continuum Mechanics, Cambridge University Press, page 20, Further, the Kronecker delta and the permutation symbol are related by the identity, known as the e {\displaystyle e} - δ {\displaystyle \delta } identity [see Problem 2.5(d)], e i j k e i m n = δ j m δ k n − δ j n δ k m {\displaystyle 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. (mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere. ==== Usage notes ==== The notation δ i j {\displaystyle \delta ^{ij}} and δ j i {\displaystyle \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 ] {\displaystyle [i=j]} . The single-argument function is equivalent to setting j = 0 {\displaystyle j=0} in the binary function. ==== Synonyms ==== (binary function): Kronecker tensor, substitution tensor ==== Derived terms ==== generalized Kronecker delta ==== Translations ==== ==== See also ==== Dirac delta Dirac delta function Dirac measure Iverson bracket Kronecker product Kronecker symbol Levi-Civita symbol === Further reading === Unit function on Wikipedia.Wikipedia Iverson bracket on Wikipedia.Wikipedia