最大特征值及其特征向量的应用

An Application Of the Maximal Eigenvalue and Its eigenvectors

矩阵的最大特征值及其特征向量反映矩阵的主要信息．文章通过建模实例介绍了最大特征值及其特征向量的应用．针对反映一组学生的各种能力的数据,进行统计分析处理,借助主成分分析法的思想,用矩阵的最大特征值及其所属的特征向量的分量的大小顺序,给出这组学生按综合能力由强到弱的排序,并用数值方法,对各种组队方案的合理性进行讨论．

The main information of a matrix is presented by its eigenvectors belonging to its maximal eigenvalue, h this pagper, an application of the maximal cigenvalue and its cigenvcctors is intreduced hy an example of medeling. Data presenting abilities for a group of students are delt with by statistical analysis. By meatus of principal component analysis, the order from strong abilities to weak abilitics for the group of students is given by the order from maximal component to minimal component of eigenvectors belonging to the maximal eigenvalue of the matrix consisiting of the data presenting abilities of the group students.