n. the function, usually denoted δ_ij, of two variables that takes the value 1 when i = j and is zero otherwise; thus the m × m identity matrix may be written as [δ_ij]_m. The generalized delta function has k subscripts and k superscripts, and is zero unless the subscripts are a permutation of the superscripts, in which case it is the signature of the permutation, and has value 1 for an even permutation and -1 for an odd permutation; when k = 3, it is sometimes written ɛ_ijk. (Named after the German algebraist, number theorist, and philosopher of mathematics Leopold Kronecker (1823-91). He was captivated by number theory while at school, and earned his doctorate while managing his family business until he retired, aged 30, and pursued mathematics full-time. He was the first critic of non-constructive existence proofs in classical analysis, sought the reconstruction of all of mathematics in terms of the positive integers, and conducted a heated correspondence with Weierstrass on these and related issues.)