Meaning of Kronecker delta | Babel Free

Definitions

1. A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
2. A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.

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.”

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

“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.”

CEFR level