利用矩阵迹求解两类正交矩阵谱的研究  

Study on solving the spectrum for two types of orthogonal matrices by matrix trace

作　　者：林志兴[1] 陈梅香[2] 杨忠鹏[1] 杨子斌 LIN Zhixing;CHEN Meixiang;YANG Zhongpeng;YANG Zibin(Fujian Key Laboratory of Financial Information Processing(Putian University),Putian 351100,China;Key Laboratory of Financial Mathematics of Fujian Province University(Putian University),Putian 351100,China;School of Mathematics and Statistics,Fuzhou University,Fuzhou 350108,China)

机构地区：[1]福建省金融信息处理重点实验室(莆田学院),福建莆田351100 [2]金融数学福建省高校重点实验室(莆田学院),福建莆田351100 [3]福州大学数学与统计学院,福州350108

出　　处：《延边大学学报（自然科学版）》2023年第4期324-332,共9页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金(61772292);福建省自然科学基金(2023J01997,2021J011103);莆田市科学技术局项目(2022SZ3001ptxy05)。

摘　　要：应用正交矩阵的特征值与迹的关系,得到了判定平方对称正交矩阵和4次方幂对称正交矩阵的充要条件.基于此,给出了这两类正交矩阵的特征值及其重数的计算公式,并利用该公式计算了已有文献中的相关数值例子.计算结果表明,该算法可不用通过求解特征多项式来求解特征值,因此该方法比传统方法简单、方便.The necessary and sufficient conditions for the judgement of two types of orthogonal matrices with square and quartic be symmetric were obtained by applying the relationship between the eigenvalues and traces of orthogonal matrices.Based on these,the calculation formulas for eigenvalues and multiplicities of these two types of orthogonal matrices were given,and be used to calculate relevant numerical examples of orthogonal matrices in the existing literatures.The results show that the algorithm is simple and convenient,as it avoids solving characteristic polynomials.The calculation results show that the algorithm can solve the eigenvalues without characteristic polynomials,thus the method is simpler and more convenient than the traditional.

关 键 词：正交矩阵 实对称矩阵 矩阵迹 谱 充要条件 特征值 

分 类 号：O151.21[理学—数学]