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.
作者
陈梅香
杨忠鹏
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)
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)。
关键词
特征值
数量对合矩阵
数量反对合矩阵
正交矩阵
迹
eigenvalue
scalar-involutory matrix
scalar-anti-involutory matrix
orthogonal matrix
trace
