浅析vandermonde行列式的性质与应用设计

浅 析 Vandermonde 行 列 式 的 性 质 与 应 用摘 要 ： 在线性代数与高等代数的学习中，行列式无疑是一个重点和难点，它是后续课程矩阵、向量空间和线性变换等的基础，且其计算具有一定的规律性和技巧性. 而Vandermonde行列式是一类很重要的行列式, 它构造独特、形式优美、性质特别，是行列式中的一颗璀璨明珠. 为了使我们对vandermonde 行列式进一步加深了解与应用，同时开阔数学视野、培育发散思维能力，以便更好地为我们的科研和生活服务，本文主要阐述了Vandermonde 行列式的证法及其相关性质, 并用例举法介绍及总结了如何利用Vandermonde 行列式计算某些特别的行列式与其在多项式、向量空间等中的简单应用.关 键 词 ： 行列式 Vandermonde Vandermonde 行列式Analysis of Vandermonde determinant Properties and ApplicationsAbstract: Linear algebra and advanced algebra learning, the determinant is undoubtedly a key and difficult points, it is the follow-up course matrix, the basis of vector spaces and linear transformations, and its calculation with a certain regularity and skill. Vandermonde determinant is a very important determinant, it constructs a unique, beautiful form of special nature, is a shining pearl in the determinant. To enable us to further deepen the understanding and application of the Vandermonde determinant, and at the same time broaden their mathematical horizons, develop divergent thinking ability in order to better serve our research and living services, the paper mainly expounds the Vandermonde determinant permit law and its related properties, and introduced with examples of France and summarizes how to use the Vandermonde determinant for the calculation of some of the special determinant of the Vandermonde determinant polynomial, the vector space.Keywords: Determinant Vandermonde Vandermonde determinant目 录1 引言..........................................................12 VANDERMONDE 行列式的定义与证法..........