群、矩阵和向量空间：线性代数的群论方法（EPUB）

English | ISBN: 0387794271 | 2017 | 427 pages | EPUB | 25 MB

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group.

英文|国际标准图书编号：0387794271 | 2017 | 427页|欧洲药典| 25 MB 这篇独特的文本为群论和线性代数提供了一种几何方法，揭示了这些学科相互作用的有趣方式。除了理解证明的概念外，这篇文章几乎不需要什么先决条件，旨在为学生提供几何和代数的坚实基础。本书从基础知识（关系、初等组合学和归纳法）开始，然后进入核心主题：群和场理论的要素（拉格朗日定理、陪集、复数和素场）、矩阵理论和矩阵群、行列式、向量空间、线性映射、本征论和对角化、约当分解和范式、正规矩阵和二次型。最后两章包括对群论的更深入的研究，强调轨道稳定器方法，以及对线性代数群的介绍，这丰富了矩阵群的概念。

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