矩阵秩的下界和特征值估计

J4 ›› 2009, Vol. 44 ›› Issue (8): 46-50.

矩阵秩的下界和特征值估计

胡兴凯伍俊良

重庆大学数理学院, 重庆 400044

收稿日期:2008-10-27 出版日期:2009-08-16 发布日期:2009-11-08
作者简介:胡兴凯(1982-),男,硕士研究生,研究方向为数值代数. Email:huxingkai84@163.com
基金资助:
重庆大学研究生科技创新基金资助项目(200801A1A0070266)

Lower bounds for the rank and estimation for eigenvalues

College of Mathematics and Physics of Chongqing University, Chongqing 400044, China

Received:2008-10-27 Online:2009-08-16 Published:2009-11-08

摘要/Abstract

摘要：

讨论了矩阵秩的下界和特征值估计,得到了矩阵秩的下界的两个估计,给出了矩阵实部和虚部的一个估计,证明了矩阵特征值都位于一个圆盘中,最后用数值算例验证了所得结果的有效性。

关键词: 矩阵;秩;特征值;F范数;估计

Abstract:

Lower bounds for the rank and the estimation for eigenvalues of matrices are discussed. Two lower bounds for the rank and estimation for the real part and imaginary part of eigenvalues are obtained. Also, we prove that all the eigenvalues of any complex matrix are located in one disk. Some numerical examples show the effectiveness of our results.

Key words: matrices; rank; eigenvalues; F norm; estimation

中图分类号:

O151.2

胡兴凯伍俊良. 矩阵秩的下界和特征值估计[J]. J4, 2009, 44(8): 46-50.

HU Xin-Kai, WU Dun-Liang. Lower bounds for the rank and estimation for eigenvalues[J]. J4, 2009, 44(8): 46-50.

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