摘要
设A,E为n×n阶矩阵,对于2个矩阵行列式之差的上界估计,有结论 det(A+E)-det(A)≤∑n i=1(n i) An-i2Ei2≤(A2+E2)n-An2.其中这里的A2表示矩阵A的谱范数.通过一种新的矩阵范数改进该结论,运用Matlab进行了实例验证,结果更优.
Let A and E be complex matrices. For the upper bounds of determinants, it have been proved that:
|det(A+E)-det(A)|≤∑(i=1→n)(i^n)||A||2^n-i||E||2^i≤(||A||2+||E||2)^n-||A||2^n
where ||A||2 is the spectral norm of A. In this note,we introduce a new norm, which improve the inequalities slightly. Finally, by using the mathematical software matlab calculation , we prove that the conclusion of this paper is better than the other results through a concrete example.
出处
《云南民族大学学报(自然科学版)》
CAS
2013年第6期422-423,共2页
Journal of Yunnan Minzu University:Natural Sciences Edition
关键词
行列式
矩阵谱范数
determinant
matrix spectral norm