数量对合矩阵与数量反对合矩阵的迹与谱  

Trace and Spectrum of Scalar-Involutory Matrices and Scalar-Anti-Involutory Matrices

作　　者：陈梅香[1,2] 杨忠鹏[2] 高洁 CHEN Meixiang;YANG Zhongpeng;GAO Jie(Key Laboratory of Financial Mathematics of Fujian Province University(Putian University),Putian,Fujian 351100,China;Putian University,Putian,Fujian 351100,China;Pingtan No.1 High School,Fuzhou,Fujian 350400,China)

机构地区：[1]金融数学福建省高校重点实验室(莆田学院),福建莆田351100 [2]莆田学院,福建莆田351100 [3]平潭第一中学,福建福州350400

出　　处：《龙岩学院学报》2024年第5期1-7,共7页Journal of Longyan University

基　　金：福建省自然科学基金(2023J01997);莆田市科技计划项目(2022SZ3001ptxy05);2023年度高等教育科学研究规划课题(23SX0315);福建省教育科学“十四五”规划2023年度课题(FJJKBK23-018)。

摘　　要：应用相似关系下保持特征值与迹不变的性质,避开了计算特征多项式,得到了数量对合矩阵和数量反对合矩阵的只用迹表示的谱、行列式的计算公式及其相似等价类。作为应用,得到了通常对合矩阵、反对合矩阵、对称正交矩阵和反对称正交矩阵的相关结论。By applying the invariant properties of eigenvalues and traces under the similar relationship,and avoiding solving characteristic polynomials,the calculation formulas for eigenvalues and determinant of the scalar-involutory matrices and scalaranti-involutory matrices,and the similar equivalence classes of the corresponding matrices determined by the trace are shown.As an application,the related conclusions of the usual involutory matrices,anti-involutory matrices,symmetric orthogonal matrices,and anti-symmetric orthogonal matrices are obtained.

关 键 词：特征值 数量对合矩阵 数量反对合矩阵 正交矩阵 迹 

分 类 号：O151.21[理学—数学]