The Exact Value of det V - n(x 1, ...,x n) and Its Applications
行列式detV_n^-(x_1,...,x_n)的准确值及其应用(英文)
摘要
Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the n× n matrix whose (i,j) th entry is N - i-1 (x j) . This paper presents a computation formula for det V - n(x 1, ...,x n) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications.
本文给出行列式Ｖ－ｎ（ｘ１，．．．，ｘｎ）的准确值，它是通常的Ｖａｎｄｅｒｍｏｄｅ行列式计算公式的推广，以及它在理论上的一些重要应用．
