| 单词 |
Kronecker delta |
| 释义 |
Kronecker delta Math.|ˈkrəʊnɛkə ˈdɛltə|
[f. the name of Leopold Kronecker (1823–91), Ger. mathematician + delta.]
A function of two integers defined as equal to one if the integers have the same value and zero otherwise; symbol δij or δji. Also (the generalized Kronecker delta), a function of 2k integers that takes the values 0 or {pm} 1 (see quot. 19272) (rare).
1927O. Veblen Invariants Quadratic Differential Forms i. 3 The theory of determinants and allied expressions is essentially a theory of alternating sets of quantities, and can be made to depend on certain fundamental alternating sets of quantities which have only the values 0 and + 1 and - 1. These sets of quantities are known as generalized Kronecker deltas because of their analogy with the Kronecker delta which is already well known. Ibid., The generalized Kronecker delta has k superscripts and k subscripts, each running from 1 to n... If the superscripts are distinct from each other and the subscripts are the same set of numbers as the superscripts, the value of the symbol is + 1 or - 1 according as an even or an odd permutation is required to arrange the superscripts in the same order as the subscripts; in all other cases its value is 0. 1937A. A. Albert Mod. Higher Algebra (1938) x. 228 Our rule for multiplying matrices implies that EijEkl = δjkEil (i,j,k,l, = 1,{ddd},s) where δ jk is the Kronecker delta. 1961P. E. Pfeiffer Linear Systems Analysis ii. 30 The value Δ of a determinant whose elements are δik is unity, where δik is the Kronecker delta. |
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