| 多项式因式分解与线性空间直和分解的关系 |
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| 引用本文： | 余兴民.多项式因式分解与线性空间直和分解的关系[J].商洛师范专科学校学报,2014(2):3-4,16. |
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| 作者姓名： | 余兴民 |
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| 作者单位： | 商洛学院数学与计算机应用学院,陕西商洛726000 |
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| 基金项目： | 商洛学院教育教学改革研究项目（13JYJX117）;商洛学院科研基金项目（09SKY005） |
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| 摘 要： | 利用线性变换的最小多项式的因式分解，得到线性空间的线性变换的不变子空间的直和分解．反过来由线性空间的任一线性变换的不变子空间的直和分解，也能得到线性变换的最小多项式的不可约因式分解，给出了相关定理及其证明。
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| 关 键 词： | 最小多项式 因式分解 线性空间 直和 |
The Relationship Between Minimal Polynomial Factorization and Direct Sum Decomposition of Linear Space |
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| YU Xing-min.The Relationship Between Minimal Polynomial Factorization and Direct Sum Decomposition of Linear Space[J].Journal of Shangluo Teachers College,2014(2):3-4,16. |
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| Authors: | YU Xing-min |
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| Institution: | YU Xing-min (College of Mathematics and Computer Application, Shangluo University, Shangluo 726000, Shaanxi) |
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| Abstract: | The decomposition of minimal polynomial factorization of linear transform is applied to, to obtain invariant subspace of linear transformation of linear space of straight and, in turn by the invariant subspace of any linear transformation of linear space direct sum decomposition, the minimal polynomial of a linear transformation of the irreducible factorization is obtained as well, with, related theorem and its proof. |
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| Keywords: | minimal polynomial factorization linear space direct sum |
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