| 一元n次多项式根的圆环覆盖定理 |
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| 引用本文： | 沈景清,曹德.一元n次多项式根的圆环覆盖定理[J].北华大学学报(社会科学版),1999(3). |
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| 作者姓名： | 沈景清 曹德 |
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| 作者单位： | 通化师范学院!通化市(沈景清)，通化市财经学校!通化市(曹德) |
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| 摘 要： | 本文的主要结果是利用相容矩阵范数的性质给出了一元ｎ次多项式根的圆环覆盖定理，即一元ｎ次多项式的所有非零复根必全都落在复平面上同一个圆环区域内．特别，ｎ次二项式的所有非零复根必都落在同一个圆周上．这一结果，可以改进盖尔斯果林（Ｇｅｒｓｓｇｏｒｉｎ）的圆盘覆盖定理的结果．
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| 关 键 词： | 矩阵范数 相容矩阵范数 向量P-范数 向量诱导的矩阵范数 矩阵谱半径 |
The Cover Theorem of the Circular Rings with Respect to the Roots of the One-variable Plolynomials of Degree n. |
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| Shen Jingqing,Cao De.The Cover Theorem of the Circular Rings with Respect to the Roots of the One-variable Plolynomials of Degree n.[J].Journal of Beihua University(Social Sciences),1999(3). |
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| Authors: | Shen Jingqing Cao De |
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| Abstract: | In this paper, utilizing the properties of the consistent matrix norms, the cover theorem of the circular rings with respect, to the roots of one-variable plolynomials of degree n is given i. e. all of the non-zero complex roots of one-variable plolynomials, of degree n. fall into the same one region of the ring on the complex plan, Especially, all of the non-zero complex roots of the binomial expressions of degree n. fall on the same one circum ference. It makes Gersgorm's theorem of circular discs be improved on. |
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| Keywords: | matrix norms Consitent matrix norms Vector p-norm Matrix norms induced by vectors Spectral radius of the matrix |
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