| 矩阵的弱迹和弱迹定理 |
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| 引用本文： | 徐帼华.矩阵的弱迹和弱迹定理[J].西安交通大学学报,1987(1). |
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| 作者姓名： | 徐帼华 |
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| 作者单位： | 西安交通大学数学系 |
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| 摘 要： | 本文首先提出了矩阵的弱迹概念,并对于一类可对称化的非对称矩降证明了两条定理,即证明弱迹均小于寻常的追迹,并大于矩阵的最大特征值。故以此弱迹作为最大特征值的上界,比追迹优越得多.应用本文的定理可以建立一系列精度越来越高的近似计算式,其精度比追迹定理所给出的值有大幅度的提高.
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| 关 键 词： | 矩阵迹 |
WEAK TRACES OF MATRIX AND THEOREMS OF WEAK TRACES |
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| Xu Guohua.WEAK TRACES OF MATRIX AND THEOREMS OF WEAK TRACES[J].Journal of Xi'an Jiaotong University,1987(1). |
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| Authors: | Xu Guohua |
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| Institution: | Department of Mathematics |
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| Abstract: | The concept of weak traces of a matrix is advanced.Proofs for two theo-
rems of weak traces concerning a kind of symmetrizable asymmetrical matrices
are given.The first theorem shows that weak treaces are always less than a
trace.The second shows that weak traces are always greater than the maxi-
mum proper value.Therefore weak traces are far betier than traces to be
used as the upper limit of the maximum proper value of a matrix.
On the basis of the theorems of weak traces,a far more precise series of
calculating formulas can be established.Even the approximate value of ma-
ximum proper value obtained by the worst one of these calculating formulas
is much better than that obtained by existing theorem of trace. |
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| Keywords: | trace of a matrix |
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