| 非正规阵的特征方下界估计及其应用 |
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| 引用本文： | 屠伯埙.非正规阵的特征方下界估计及其应用[J].复旦学报(自然科学版),1987(2). |
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| 作者姓名： | 屠伯埙 |
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| 作者单位： | 复旦大学数学系 |
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| 摘 要： | 本文推广与改进了关于特征方下界的Henrici不等式,提供了实特征方与虚特征方的下界估计.应用这些估计式,推导出了矩阵的展形与秩的下界,并由此得出了判断方阵非异性的一些充分条件.
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| 关 键 词： | 非正规阵 下界 特征方 展形 秩 |
LOWER BOUNDS FOR THE CHARACTERISTIC SQUARES OF NONNORMAL MATRICES AND THEIR APPUCATIONS |
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| Tu Boxun.LOWER BOUNDS FOR THE CHARACTERISTIC SQUARES OF NONNORMAL MATRICES AND THEIR APPUCATIONS[J].Journal of Fudan University(Natural Science),1987(2). |
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| Authors: | Tu Boxun |
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| Institution: | Department of Mathematics |
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| Abstract: | This paper generalizes and improves Herici's inequality for the lower bound of the "characteristic square" of a nonnormal matrix and presents an estimate for the lower bounds of both the real and imaginary characteristic squares. By applying the improved inequalities, a number of consequences are deduced on the lower bounds for the spread and the rank of nonnormal matrices, which leads to some sufficient conditions for determining the nonsingularity of nonnormal matrices. |
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| Keywords: | nonnormal matrix lower bound characteristic square spread rank |
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