Schur矩阵[Schur Matrix] - 达人(其实～我是卧底，来自外星)

2005/09/05 | Schur矩阵[Schur Matrix]
类别(∑〖数学〗) | 评论(0) | 阅读(215) | 发表于 20:42: The square matrix formed by setting , where is a th root of unity. The Schur matrix has a particularly simple determinant given by
(1)

where is an odd prime and
(2)

This determinant has been used to prove the quadratic reciprocity law (Landau 1958, Vardi 1991). The absolute values of the permanents of the Schur matrix of order are given by 1, 3, 5, 105, 81, 6765, ... (Sloane's A003112, Vardi 1991).
Denote the Schur matrix with the first row and first column omitted by . Then
(3)

where perm denoted the permanent (Vardi 1991).; 0