一类矩阵奇异空间的扰动  

Perturrbations about Sngular Space

作　　者：陈建新[1] 

机构地区：[1]广东工业大学应用数学学院,广东广州510520

出　　处：《中北大学学报（自然科学版）》2013年第2期117-119,共3页Journal of North University of China(Natural Science Edition)

摘　　要：为了得到列满秩矩阵的奇异空间的扰动界,结合矩阵2-范数和F-范数的性质以及范数与特征值间的关系,利用矩阵等式等价变换的方法和技巧,在现有研究的基础上讨论了列满秩矩阵的奇异空间的扰动问题,得到了该类矩阵的奇异空间扰动界.将本文主要定理得到的界的因子maxσi/min～σj与相应文献的结果中因子1/(1-3δ)～(1/2)相比较,并通过具体数值例子比较得出本文得到的界在maxσi/max～σj<1时更优.By using the method of matrix equation equivalent transformation,we had considered the singular space perturbation about column full rank matrix.Combining the properties between F-norm,2-norm and the Eigenvalues,the bound about singular space was obtained.Finally,we make the comparison between our result and the 1/（1-3δ）～（1/2） in corresponding paper.In the case of maxσi/minj＆lt;1,our bound is more ideal than that in corresponding paper.At last,a numerical example was given to compare our results with the corresponding result.

关 键 词：奇异空间 范数 扰动界 

分 类 号：O241.1[理学—计算数学]