一类特殊对称矩阵的逆特征值求解方法  

Inverse Eigenvalue Method for A Special Symmetric Matrix

作　　者：王师 陈学斌 WANG Shi;CHEN Xue-bin(Hainan Vocational University of Science and Technology,Haikou 571126,China;College School of Science,North China University of Science and Technology,Tangshan 063210,China;Hebei Province Key Laboratory of Data Science and Application(North China University of Science and Technology),Tangshan 063210,China;Tangshan Data Science Laboratory(North China University of Science and Technology),Tangshan 063210,China)

机构地区：[1]海南科技职业大学公共教学部,海南海口571126 [2]华北理工大学理学院,河北唐山063210 [3]河北省数据科学与应用重点实验室(华北理工大学),河北唐山063210 [4]唐山市数据科学重点实验室(华北理工大学),河北唐山063210

出　　处：《数学的实践与认识》2021年第24期293-297,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61170317,61170254)。

摘　　要：给出一类特殊对称矩阵的形式,提出和证明这类特殊对称矩阵的性质.在给定的条件下,推导证明此类特殊对称矩阵存在性和唯一性的充要条件,进而给出求解这类特殊对称矩阵的逆特征值求解算法和矩阵的解析式.最后,通过数值算例验证算法的可行性和有效性.In this paper,the form of a special symmetric matrix is given,and the properties of this kind of special symmetric matrix are proved.Under the given conditions,the sufficient and necessary conditions for the existence and uniqueness of this kind of special symmetric matrix are derived,and then the algorithm for solving the inverse eigenvalue of a special symmetric matrix and the analytical formula of the matrix are given.Finally,a numerical example is given to verify the feasibility and effectiveness of the algorithm.

关 键 词：特殊对称矩阵 逆特征值 特征向量 矩阵分解 

分 类 号：O151.21[理学—数学]