Kronecker delta

English Etymology en Leopold Kronecker German mathematician 1823 1891 = Noun en mathematics A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise. en 1998 Robert G. Deissler Turbulent Fluid Motion https://books.google.com.au/books?id=p5WGgKEq85oC&pg=PA24&dq=%22Kronecker+delta%22%7C%22Kronecker+deltas%22&hl=en&sa=X&ved=0ahUKEwiHtJLnmOzcAhXK5oMKHREsDgYQ6AEIKjAB#v=onepage&q=%22Kronecker%20delta%22%7C%22Kronecker%20deltas%22&f=false 24 Taylor & Francis The Kronecker delta is an example of an isotropic tensor. That is, its components remain invariant with rotation of coordinate axes. 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 - identity [see Problem 2.5(d)], .      (2.2.43) The permutation symbol and the Kronecker delta prove to be very useful in proving vector identities. en 2017 Sadri Hassani Special Relativity: A Heuristic Approach https://books.google.com.au/books?id=GPTtDQAAQBAJ&pg=PA257&dq=%22Kronecker+delta%22%7C%22Kronecker+deltas%22&hl=en&sa=X&ved=0ahUKEwiHtJLnmOzcAhXK5oMKHREsDgYQ6AEI7wEwIQ#v=onepage&q=%22Kronecker%20delta%22%7C%22Kronecker%20deltas%22&f=false 257 Elsevier 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 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 is replaced by the other index of the Kronecker delta. en mathematics A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere. Usage notes The notation and 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 . The single-argument function is equivalent to setting in the binary function. Synonyms binary function en Kronecker tensor, en substitution tensor Derived terms en generalized Kronecker delta Translations Chinese: Mandarin: cmn 克羅內克爾δ Kèluónèikè'ěr δ See also en Dirac delta en Dirac delta function en Dirac measure en Iverson bracket en Kronecker product en Kronecker symbol en Levi-Civita symbol Further reading Unit function Iverson bracket