不同对角矩阵的特征值求解  

Eigenvalue Solution of Different Diagonal Matrices

作　　者：田金玲 TIAN Jinling(Department of Mathematics,Datong Normal College,Datong 037000,China)

机构地区：[1]大同师范高等专科学校数学系,山西大同037000

出　　处：《山东航空学院学报》2024年第6期91-97,120,共8页Journal of Binzhou University

摘　　要：利用分块矩阵的性质,结合分块上三角矩阵,给出了次对角矩阵的特征值求解公式;利用迭代递推的方法给出了三对角矩阵的特征值求解公式;证明了2 n+1阶三对角矩阵与n阶三对角矩阵的特征值的关系,并应用降低行列式阶数的办法求出了高阶矩阵的部分特征值。By utilizing the properties of block matrices and combining with block upper triangular matrices,a formula for solving the eigenvalues of sub diagonal matrices was given;a formula for solving the eigenvalues of a tridiagonal matrix was given using iterative recursion;the relationship between the eigenvalues of a 2 n+1 order tridiagonal matrix and an n order tridiagonal matrix was proved,and some eigenvalues of a higher-order matrix were obtained by reducing the order of the determinant.

关 键 词：次对角矩阵 三对角矩阵 分块矩阵 特征多项式 特征值 

分 类 号：O151.21[理学—数学]