R-对称矩阵的左右逆特征值问题及其可解条件
he solvability conditions for left and right inverse eigenvalue problems of R-symmetric matrices
实矩阵R是对称非平凡对合矩阵,实矩阵A称为是R对称矩阵,若RAR=A.本文研究了R对称矩阵的左右逆特征值问题,得到可解条件及解的表达式,并讨论了对任意给定矩阵的最佳逼近问题.最后,给出数值例子.我们的结论推广了李范良的文章:反中心对称矩阵的左右逆特征值问题.
Let real matrix R be a symmetric and nontrivial involution. Real matrix A is called R-symmetric matrix if RAR = A. In this paper, the left and right inverse eigenvalue problem for R-symmetric matrices is studied. We obtain the solvability conditions and the solution expression of that. Furthermore, the optimal approximation problem for given matrix is also discussed. Finally, some numerical examples are given. Our conclusions extend that of Fan-liang Li\\\\\\\
尤传华、沈凯娟、杜玉霞
数学
R-对称矩阵左右特征值对最佳逼近
R-symmetric matrixLeft and right eigenpairsOptimal approximation
尤传华,沈凯娟,杜玉霞.R-对称矩阵的左右逆特征值问题及其可解条件[EB/OL].(2008-03-17)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/200803-414.点此复制
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