Kronecker delta

Noun

 * 1)  A binary function, written as &delta; with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
 * 2) * 2007, J. N. Reddy, An Introduction to Continuum Mechanics,, 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.
 * 1)  A unary function, written as &delta; with a single index, which evaluates to 1 at zero, and 0 elsewhere.
 * 1)  A unary function, written as &delta; with a single index, which evaluates to 1 at zero, and 0 elsewhere.
 * 1)  A unary function, written as &delta; with a single index, which evaluates to 1 at zero, and 0 elsewhere.

Usage notes

 * The notation $$\delta^{ij}$$ and $$\delta^i_j$$ 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.

Translations

 * Chinese:
 * Mandarin: 克羅內克爾δ