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2个矩阵行列式之差上界的新估计

The new estimation of upper bounds for determinants of two matrices
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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
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参考文献5

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二级参考文献1

  • 1张禾瑞.高等代数[M].北京:高等教育出版社,2005.

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