矩阵的秩和非零特征值个数关系的进一步讨论 |
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引用本文: | 梁小春,;陈梅香,;杨忠鹏,;陈清华.矩阵的秩和非零特征值个数关系的进一步讨论[J].漳州师院学报,2014(2):1-6. |
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作者姓名: | 梁小春 ;陈梅香 ;杨忠鹏 ;陈清华 |
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作者单位: | [1]福州大学数学与计算机科学学院,福建福州350108; [2]莆田学院数学学院,福建莆田351100; [3]闽南师范大学数学与统计学院,福建漳州363000; [4]福建师范大学数学与计算机科学学院,福建福州350007 |
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基金项目: | 国家自然科学基金(11071040); 2008年福建省高校服务海西建设重点项目(2008HX03); 福建省教育厅科研基金项目(JA12286,JB12169); 莆田学院教学研究项目(JG2012021) |
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摘 要: | 本文给出了矩阵的秩和非零特征值个数的差的等式与不等式,并讨论这个不等式的上下界等式成立的多角度的等价描述.
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关 键 词: | 矩阵秩 非零特征值 矩阵指数 GP矩阵 |
Some Further Discussions on the Relationship between Ranks and Numbers of Non-zero Eigenvalues of Matrices |
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Institution: | LIANG Xiao-chun, CHEN Mei-xiang, YANG Zhong-peng, CHEN Qin-hua (1.College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350108, China; 2.School of Mathematics, Putian Universtiy, Putian, Fujian 351100, China; 3.School of Mathematics and Statistics, Minnan Normal Universtiy, Zhangzhou, Fujian 363000, China; 4.College of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China) |
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Abstract: | In this paper, some equalities and inequalities for difference of rank and number of non-zero eigenvalues of a matrix are given out, then for them, the multiangular equivalent characterizations for the equation case of upper and lower bound are discussed. |
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Keywords: | rank of a matrix non-zero eigenvalue matrix index GP-matrix |
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