2n阶实对称循环矩阵的性质与应用  

The properties and applications of 2n order real symmetric recurrent 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：《河南工程学院学报（自然科学版）》2024年第3期74-80,共7页Journal of Henan University of Engineering：Natural Science Edition

摘　　要：以偶数阶数为切入点,利用矩阵分块的办法,2n阶实对称循环矩阵可以分块成分块全对称矩阵,存在正交矩阵可以将2n阶实对称循环矩阵准对角化,得到2n阶实对称循环矩阵的行列式、逆矩阵、特征值的简便计算公式。Taking even order as the starting point,using the method of matrix partitioning,a 2n order real symmetric cyclic matrix can be partitioned into block wise fully symmetric matrices.There exists an orthogonal matrix that can quasi diagonalize 2n order real symmetric cyclic matrices.A simple formula for calculating the determinant,inverse matrix,and eigenvalues of a 2n order real symmetric recurrent matrix.

关 键 词：对称循环矩阵 对称矩阵 对角化 行列式 逆矩阵 特征值 

分 类 号：O151.21[理学—数学]