王全龙.行列式detVn-(x1,...,xn)的准确值及其应用(英文)[J].数学研究及应用,1998,18(4):513~519 |
行列式detVn-(x1,...,xn)的准确值及其应用(英文) |
The Exact Value of det Vn-(x1,...,xn) and Its Applications |
投稿时间:1995-10-29 |
DOI:10.3770/j.issn:1000-341X.1998.04.006 |
中文关键词: |
英文关键词:generalized Vandermonde determinant computation formula generalized Vandermonde matrix rank Tcbebycheff system. |
基金项目: |
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中文摘要: |
本文给出行列式Vn-(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. |
英文摘要: |
Suppose that x is a complex number and i is a non negative integer. Define Ni-(x)=|x|i if i is even and Ni-(x)=x|x|i-1 if i is odd. Let Vn-(x1,...,xn) denote the n× n matrix whose (i,j) th entry is Ni-1-(xj) . This paper presents a computation formula for det Vn-(x1,...,xn) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications. |
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