| 矩阵的特征值定位和非奇异性判定 |
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| 引用本文： | 桑彩丽,赵建兴.矩阵的特征值定位和非奇异性判定[J].吉林大学学报(理学版),2019,57(4):853-856. |
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| 作者姓名： | 桑彩丽 赵建兴 |
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| 作者单位： | 贵州民族大学数据科学与信息工程学院,贵阳,550025;贵州民族大学数据科学与信息工程学院,贵阳,550025 |
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| 基金项目： | 国家自然科学基金;贵州省教育厅科技拔尖人才支持项目;贵州省科技计划 |
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| 摘 要： | 通过将复方阵A分裂为A=sI-B(其中: s为任意复数; I为单位矩阵; B为复方阵), 利用矩阵非奇异性判定已有的方法, 得到了A的含有两个参数（s和正整数k）的特征值包含集和非奇异性的判定方法, 并证明所得特征值包含集和非奇异性判定方法比已有结果更精确、 更具一般性. 数值结果表明, 通过调节s和k, 可以对A的特征值进行更精确定位, 从而判定A的非奇异性.
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| 关 键 词： | 矩阵 特征值 定位 非奇异性 判定 |
| 收稿时间： | 2018-08-04 |
Eigenvalue Localization and Determination of Non singularity for Matrices |
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| SANG Caili,ZHAO Jianxing.Eigenvalue Localization and Determination of Non singularity for Matrices[J].Journal of Jilin University: Sci Ed,2019,57(4):853-856. |
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| Authors: | SANG Caili ZHAO Jianxing |
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| Institution: | College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
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| Abstract: | By splitting a complex square matrix A=sI-B, where s is an arbitrary complex number, I is the identity matrix and B is a complex square matrix, and by using an existing method of determination of non singularity for matrices, some eigenvalue inclusion sets and some methods of determination of non singularity for A with two parameters (s and a positive integer k) are obtained and proved to be more accurate and more general than some existing results. Numerical results show that by adjusting s and k, the eigenvalues of A can be located more accurate, and the non singularity of A can be determined. |
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| Keywords: | matrix eigenvalue localization non singularity determination |
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