毕业论文—浅析vandermonde行列式的性质与应用

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1、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

2、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行列式宁夏师范学院2012届本科毕业生毕业论文AnalysisofVandermondedeterminantPropertiesandApplicationsAbstract:Linearalgebraandadvancedalgebralearning,thedeterminantisundoubtedlyakeyanddifficultpoints,itisthefollow-upcoursematrix,thebasisofvectors

3、pacesandlineartransformations,anditscalculationwithacertainregularityandskill.Vandermondedeterminantisaveryimportantdeterminant,itconstructsaunique,beautifulformofspecialnature,isashiningpearlinthedeterminant.ToenableustofurtherdeepentheunderstandingandapplicationoftheVandermond

4、edeterminant,andatthesametimebroadentheirmathematicalhorizons,developdivergentthinkingabilityinordertobetterserveourresearchandlivingservices,thepapermainlyexpoundstheVandermondedeterminantpermitlawanditsrelatedproperties,andintroducedwithexamplesofFranceandsummarizeshowtousethe

5、VandermondedeterminantforthecalculationofsomeofthespecialdeterminantoftheVandermondedeterminantpolynomial,thevectorspace.Keywords:DeterminantVandermondeVandermondedeterminant宁夏师范学院2012届本科毕业生毕业论文目录1引言................................................................................

6、.....................................................12VANDERMONDE行列式的定义与证法.............................................................................22.1VANDERMONDE行列式的定义......................................................................................22.2VANDERMONDE行列式的证

7、法......................................................................................23VANDERMONDE行列式的性质..........................................................................................43.1VANDERMONDE行列式的翻转与变形...........................................................

8、..............43.2VANDERMONDE行列式为0的充分必要条件......