Kronecker, Leopold (1823-1891)

German mathematician who devised the Kronecker delta in linear algebra. He attempted to unify analysis, algebra, and elliptical functions.

Kronecker was born at Liegnitz (now Legnica, Poland), and studied at Berlin, Bonn, and Breslau. Financially independent, he devoted himself to research and lectured at Berlin from 1861. In 1883 he became professor there.

Kronecker was obsessed with the idea that all branches of mathematics (apart from geometry and mechanics) should be treated as parts of arithmetic. He also believed that whole numbers were sufficient for the study of mathematics - ‘The whole numbers has the Dear God made; all else is man's work’.

Kronecker published a system of axioms in 1870, later shown to govern finite Abelian groups.

The Kronecker delta is denoted by δrs, for which δrs = 0 when r ≠ s and δrs = 1 when r = s, where r, s are 1, 2, 3, ... He found this a useful device in the evaluation of determinants, the r and s being concerned with a row and a column of the determinant.