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.
作者
田金玲
TIAN Jinling(Department of Mathematics,Datong Normal College,Datong 037000,China)
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
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
sub-diagonal matrix
three diagonal short matrix
block matrix
characteristic polynomials
eigenvalues
