| 投影广义对称矩阵逆特征值问题可解性条件及最佳逼近 |
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| 引用本文： | 梁茂林,尤传华,周海林. 投影广义对称矩阵逆特征值问题可解性条件及最佳逼近[J]. 甘肃科学学报, 2007, 19(3): 1-3 |
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| 作者姓名： | 梁茂林 尤传华 周海林 |
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| 作者单位： | 1. 天水师范学院,数理与信息科学学院,甘肃,天水,741001;兰州大学,数学与统计学院,甘肃,兰州,730000
2. 兰州大学,数学与统计学院,甘肃,兰州,730000 |
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| 摘 要： | 研究了投影矩阵的结构,给出投影变换下一类广义对称矩阵(即投影广义对称矩阵)的概念及结构,讨论了此类广义对称矩阵逆特征值问题有解的充要条件,并给出通解的表达式;同时也考虑了对于给定矩阵的最佳逼近问题.
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| 关 键 词： | 投影矩阵 投影广义对称矩阵 逆特征值问题 最佳逼近 |
| 文章编号： | 1004-0366（2007）03-0001-03 |
| 收稿时间： | 2006-08-15 |
| 修稿时间： | 2006-08-15 |
The Solvability Conditions for the Inverse Eigenvalue Problem and Associated Approximation Problems of Generalized Symmetric Matrices under Projective Transformation |
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| LIANG Mao-lin,YOU Chuan-hua,ZHOU Hai-lin. The Solvability Conditions for the Inverse Eigenvalue Problem and Associated Approximation Problems of Generalized Symmetric Matrices under Projective Transformation[J]. Journal of Gansu Sciences, 2007, 19(3): 1-3 |
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| Authors: | LIANG Mao-lin YOU Chuan-hua ZHOU Hai-lin |
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| Affiliation: | 1. College of Mathematics, Physics and Information Science, Tianshui Normal College, Tianshui 741001, China ; 2. Institute of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China |
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| Abstract: | The structures of the projective matrix and generalized projective symmetric matrix are studied. The solvability conditions of the inverse eigenvalue problem for generalized projective symmetric matrix are discussed, and its general solution is derived. Meanwhile ,the associated optimal approximation problem for a given matrix is also considered. |
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| Keywords: | projective matrix generalized projective symmetric matrix inverse eigenvalue problem optimal approximation |
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