| 幂零--中心化方法 |
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| 引用本文： | 高玉斌,邵燕灵.幂零--中心化方法[J].数学研究及应用,2014,34(5):597-607. |
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| 作者姓名： | 高玉斌 邵燕灵 |
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| 作者单位： | 中北大学数学系, 山西 太原 030051;中北大学数学系, 山西 太原 030051 |
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| 基金项目： | 国家自然科学基金(Grant No.11071227);山西省回国留学人员科研资助项目(Grant No.12-070). |
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| 摘 要： | An nxn complex sign pattern(ray pattern) S is said to be spectrally arbitrary if for every monic nth degree polynomial f(λ) with coefficients from C,there is a complex matrix in the complex sign pattern class(ray pattern class) of S such that its characteristic polynomial is f(λ).We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns,respectively.We find that the Nilpotent-Centralizer methods for three kinds of patterns(sign pattern,complex sign pattern,ray pattern) are the same in form.
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| 关 键 词： | 幂零 扶正 标志图案 特征多项式 射线 复数 线图 |
| 收稿时间： | 2013/10/28 0:00:00 |
| 修稿时间： | 2014/6/18 0:00:00 |
The Nilpotent-Centralizer Methods |
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| Yubin GAO and Yanling SHAO.The Nilpotent-Centralizer Methods[J].Journal of Mathematical Research with Applications,2014,34(5):597-607. |
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| Authors: | Yubin GAO and Yanling SHAO |
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| Institution: | Department of Mathematics, North University of China, Shanxi 030051, P. R. China;Department of Mathematics, North University of China, Shanxi 030051, P. R. China |
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| Abstract: | An $n \times n$ complex sign pattern (ray pattern) ${\cal S}$ is said to be spectrally arbitrary if for every monic $n$th degree polynomial $f(\lambda)$ with coefficients from $\mathbb{C}$, there is a complex matrix in the complex sign pattern class (ray pattern class) of ${\cal S}$ such that its characteristic polynomial is $f(\lambda)$. We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns, respectively. We find that the Nilpotent-Centralizer methods for three kinds of patterns (sign pattern, complex sign pattern, ray pattern) are the same in form. |
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| Keywords: | complex sign pattern ray pattern spectrally arbitrary pattern nilpotence |
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