共查询到18条相似文献,搜索用时 234 毫秒
1.
用构造性方法证明了以同一个特征向量为终端向量的Jordan链从始端向量到终端向量可以有不同的最大长度,并给出了Jordan基中Jordan链的某些性质,进一步完善了Jordan标准形过渡矩阵求法的补充条件. 相似文献
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用构造性方法证明了以同一个特征向量为终端向量的Jordan链从始端向量到终端向量可以有不同的最大长度,并给出了Jordan基中Jordan链的某些性质,进一步完善了Jordan标准形过渡矩阵求法的补充条件. 相似文献
3.
复向量空间的分解与复线性变换的Jordan标准形* 总被引:1,自引:0,他引:1
本文引入表征复线性变换结构的新对象。这些新对象给出复向量空间关于复线性变换分解的新结果且给出构造Jordan标准形的所有Jordan基。因而,它们能够直接导致着名的Jordan定理及空间的第三分解定理,且能给出对Jordan形精致微妙结构的新的深刻洞察。后者表明,复线性变换的Jordan标准形是一种在双重任意选择下具有不变性的结构。 相似文献
4.
本对Jordan标准形定理给出了一种使用初等变换的证明,直观意义明显、易于理解,可用于线性代数教学。 相似文献
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本文对 Jordan标准形定理给出了一种使用初等变换的证明 ,直观意义明显、易于理解 ,可用于线性代数教学 . 相似文献
6.
本文直接根据线性变换给出了Fiting定理的一个证明,并用它建立了定理1,从而得到一种在相似变换下化简的准对角矩阵,然后在定理2中讨论该准对角矩阵与Jrodan标准形的关系及其应用. 相似文献
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Hamilton-Cayley定理是《高等代数》中最基本与深刻的定理之一,也是其中课程中知识与方法的集散点之一.它的证明方式涉及几乎所有《高等代数》的知识,引伸出的涵义也多种多样.文中回顾了Cayley,Hamilton与Frobenius的三种原始证明,并梳理了目前《高等代数》教材中的数种证明,最后讨论不同证明之间的联系. 相似文献
11.
Moshe Roitman 《Linear and Multilinear Algebra》1999,46(3):245-247
We present a short proof of the Jordan Decomposition Theorem 相似文献
12.
We study codes over Frobenius rings. We describe Frobenius rings via an isomorphism to the product of local Frobenius rings
and use this decomposition to describe an analog of linear independence. Special attention is given to codes over principal
ideal rings and a basis for codes over principal ideal rings is defined. We prove that a basis exists for any code over a
principal ideal ring and that any two basis have the same number of vectors.
Hongwei Liu is supported by the National Natural Science Foundation of China (10571067). 相似文献
13.
Commutative Rings, by Irving Kaplansky. Revised edition. The University of Chicago Press, Chicago and London, 1974, ix+182pp.($9.75) Symmetry Groups and their Applications, by Willard Miller, Jr. Academic Press. 相似文献
14.
Luc Bélair 《Journal of Algebra》2009,321(9):2353-2364
We prove an approximation property for solutions to difference equations in excellent discrete valuation rings satisfying an appropriate Hensel's lemma, analog to a theorem of Greenberg [M. Greenberg, Rational points in henselian discrete valuation rings, Publ. Math. Inst. Hautes Études Sci. 31 (1966) 59–64]. In the case of Witt vectors we obtain a Nullstellensatz for Frobenius algebraic equations. 相似文献
15.
Luc Bélair 《Comptes Rendus Mathematique》2005,340(2):99-102
We prove an approximation property for Frobenius difference equations in the Witt vectors, analog to a theorem of Greenberg [Publ. Math. IHES 31 (1966) 59–64]. To cite this article: L. Bélair, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
16.
The notion of a Z-algebra has a non-linear analogue, whose purpose it is to control operations on commutative rings rather than linear operations on abelian groups. These plethories can also be considered non-linear generalizations of cocommutative bialgebras. We establish a number of category-theoretic facts about plethories and their actions, including a Tannaka-Krein-style reconstruction theorem. We show that the classical ring of Witt vectors, with all its concomitant structure, can be understood in a formula-free way in terms of a plethystic version of an affine blow-up applied to the plethory generated by the Frobenius map. We also discuss the linear and infinitesimal structure of plethories and explain how this gives Bloch's Frobenius operator on the de Rham-Witt complex. 相似文献
17.
Yunkai Zhou 《Applied mathematics and computation》2011,217(24):10267-10270
We study the eigenvalues of a matrix A perturbed by a few special low-rank matrices. The perturbation is constructed from certain basis vectors of an invariant subspace of A, such as eigenvectors, Jordan vectors, or Schur vectors. We show that most of the eigenvalues of the low-rank perturbed matrix stayed unchanged from the eigenvalues of A; the perturbation can only change the eigenvalues of A that are related to the invariant subspace. Existing results mostly studied using eigenvectors with full column rank for perturbations, we generalize the results to more general settings. Applications of our results to a few interesting problems including the Google’s second eigenvalue problem are presented. 相似文献
18.
O. A. Veliev 《Mathematical Notes》2007,81(3-4):440-448
We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm-Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis. 相似文献