Kronecker delta

plural Kronecker deltas

1. mathematicsA binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.

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

   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-δ identity [see Problem 2.5(d)], e_ijke_imn=δⱼₘδₖₙ-δⱼₙδₖₘ. (2.2.43)

   2 more examples

   The Kronecker delta #92;delta#95;#123;ij#125; is an example of an isotropic tensor. That is, its components remain invariant with rotation of coordinate axes.

   1998, Robert G. Deissler, Turbulent Fluid Motion, Taylor & Francis, page 24

   The most important property of the Kronecker delta occurs when it shares a common repeated index with another tensor: Note 10.1.3. When an index of a tensor T is contracted with one of the indices of the Kronecker delta, the result is an expression in which the Kronecker delta is removed and the contracted index of T is replaced by the other index of the Kronecker delta.

   2017, Sadri Hassani, Special Relativity: A Heuristic Approach, Elsevier, page 257

   Synonyms: Kronecker tensor, substitution tensor

2. mathematicsA unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.