宁夏师范学院2012届本科毕业生毕业论文浅析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、性质特殊，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、培养发散思维能力，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行列式计算某些特殊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VandermondeVandermonde行列式AnalysisofVandermondedeterminantPropertiesandApplicationsAbstract:Linearalgebraandadvancedalgebralearning,thedeterminantisundoubtedlyakeyanddifficultpoints,itisthefollow-upcoursematrix,thebasisofvectorspacesandlineartransformations,anditscalculationwithacertainregularityandskill.Vandermondedeterminantisaveryimportantdeterminant,itconstructsaunique,beautifulformofspecialnature,isashiningpearlinthedeterminant.ToenableustofurtherdeepentheunderstandingandapplicationoftheVandermondedeterminant,andatthesametimebroadentheirmathematicalhorizons,developdivergentthinkingabilityinordertobetterserveourresearchandlivingservices,thepapermainlyexpoundstheVandermondedeterminantpermitlawanditsrelatedproperties,andintroducedwithexamplesofFranceandsummarizeshowtousetheVandermondedeterminantforthecalculationofsomeofthespecialdeterminantoftheVandermondedeterminantpolynomial,thevectorspace.Keywords:DeterminantVandermondeVandermondedeterminant目录TOC\o"1-3"\h\z\uHYPERLINK\l"_Toc326066946"1引言PAGEREF_Toc326066946\h1HYPERLINK\l"_Toc326066947"2Vandermonde行列式的定义与证法PAGEREF_Toc326066947\h2HYPERLINK\l"_Toc326066948"2.1Vandermonde行列式的定义PAGEREF_Toc326066948\h2HYPERLINK\l"_Toc326066949"2.2Vandermonde行列式的证法PAGEREF_Toc326066949\h2HYPERLINK\l"_Toc326066950"3Vandermonde行列式的性质PAGEREF_Toc326066950\h4HYPERLINK\l"_Toc326066951"3.1Vandermonde行列式的翻转与变形PAGEREF_Toc326066951\h4HYPERLINK\l"_Toc326066952"3.2Vandermonde行列式为0的充分必要条件PAGEREF_Toc326066952\h5HYPERLINK\l"_Toc326066953"3.3Vandermonde行列式推广的性质定理PAGEREF_Toc326066953\h5HYPERLINK\l"_Toc326066954"4Vandermonde行列式的应用PAGEREF_Toc3260