一类矩阵奇异空间的扰动

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一类矩阵奇异空间的扰动

更新时间：2026-09-14

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～σj1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/minj1

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.

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Related Author

张晋珠

Related Institution

中北大学分校基础部

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