对箭矩阵的两类广义逆问题  

Two kinds of generalized inverse problems of arrow matrix

作　　者：雷英杰[1] 崔萌 LEI Yingjie;CUI Meng(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《安徽大学学报（自然科学版）》2022年第6期1-7,共7页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12071444);山西省自然科学基金资助项目(201801D121153)。

摘　　要：研究一类对箭矩阵的对称与非对称形式.问题1利用箭型矩阵的相关性质,将该矩阵的每个顺序主子式的最大、最小特征值作为其特征数据,得到了问题可解的充要条件并给出矩阵的对称构造;问题2在问题1的基础上进行改进,通过加入矩阵的一组特征对作为条件,得到问题有唯一解的充要条件并给出非对称构造.最后给出解的表达式以及数值实例,验证了结果的准确性.The symmetric and asymmetric forms of an arrow matrix were studied. The first problem used the related properties of the arrow matrix and principal submatrices’ the maximum and minimum eigenvalues as its characteristic data to obtain the necessary and sufficient conditions for the problem’s solution, and given the symmetric construction of the matrix;the second problem was improved on the basis of the first problem. By adding a set of characteristic pairs of the matrix as the condition, the necessary and sufficient condition for the unique solution of the problem was obtained and the asymmetric structure was given. At last, the expressions of solutions and numerical examples were given for both problems, which verified the accuracy of the results.

关 键 词：特征对 主子矩阵 特征值的交错性 逆特征值 

分 类 号：O157[理学—数学]