对于毕业论文 幂零矩阵的性质与应用 曹彦辉

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1、对于毕业论文幂零矩阵的性质与应用曹彦辉对于毕业论文幂零矩阵的性质与应用曹彦辉导读：·31.2引理··············································································································································-4-1.2幂零矩阵的判别与构建·····················································································

2、····························齐齐哈尔大学毕业设计（论文）摘要在高等数学研究中，矩阵不仅是研究问题的一种重要工具而且在实际生活中具有广泛的应用,幂零矩阵是矩阵中满足Ak?0的一类比较特殊的矩阵，所以幂零矩阵在矩阵理论中占有非常重要的地位，同时在实际应用方面也具有特殊的意义。幂零矩阵具有很多很好的性质，本文归纳总结18条性质，共用到定理或引理14条，系统说明这些性质并给出相应的证明；如在求特殊矩阵的逆以及在若尔当标准型的计数方面等，本文深入挖掘这些性质，并且用不同的方法去分析、论证这些性质。同时本文幂零矩阵自身具有的一些特殊性质给出了论证，并举例加以说

3、明。本文同时探讨了2个矩阵是幂零矩阵的充分必要条件，并说明其在求矩阵的逆矩阵方面的方便化与简单化，体现了幂零矩阵的实用性以及研究的必要行；同时探讨了数域K上n阶矩阵与幂零矩阵简单的联系，比如可以利用n阶矩阵与幂零矩阵的运算解决需许多实际问题，即每一个奇异方阵均可表示成一个幂零方阵加上两个幂零方阵的乘积.利用幂零矩阵的性质，可以把一个n阶方阵变为两个可逆矩阵与一个对角矩阵之和，进而方便研究矩阵的其他性质,并通过具体例子说明其在实际应运中的作用。关键词：幂零矩阵；线性变换；逆矩阵；若尔当标准型；特征值齐齐哈尔大学毕业设计（论文）AbstractMatrixactsasakeyro

4、leinstudyingandsolvingthequestionsinadvancedmathematics.Asspecialformsofmatrix,nilpotentmatricesplayakeyrolenotonlyinthetheoryofmatrixbutalsoinpracticalapplication.NilpotentMatriceshavemanygoodproperties.Inthepaper,ethodsthesepropertiesinprofundity.Thepapereuniquepropertiesofnilpotentmatric

5、esanddiscussesthenecessaryandsufficientconditionofnilpotentmatrices.Thenthepapershoatrix,andexplainsitspracticalapplicationbyexamples.Keyatrix；Lineartransformation；Inversematrix；Jordancanonicalform；Characteristic齐齐哈尔大学毕业设计（论文）目录摘要·····························································

6、·····································································································IAbstract··························································································································································II绪论·······················

7、··········································································································································11.1概念··············································································································