| 单词 | generalized kronecker delta |
| 释义 | > as lemmasgeneralized Kronecker 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 ± 1 (see quot. 19272) (rare). ΚΠ 1927 O. 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. 1927 O. Veblen Invariants Quadratic Differential Forms i. 3 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. 1937 A. A. Albert Mod. Higher Algebra (1938) x. 228 Our rule for multiplying matrices implies that EijEkl = δjkEil (i,j,k,l, = 1,…,s) where δjk is the Kronecker delta. 1961 P. E. Pfeiffer Linear Syst. Anal. ii. 30 The value Δ of a determinant whose elements are δik is unity, where δik is the Kronecker delta. < as lemmas |
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