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线性代数 Linear Algebra 英文原版

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作者Robert J Valenza

出版社Springer

ISBN9781461269403

出版时间2012-10

印刷时间2012-10

印数1千册

装帧平装

开本32开

纸张轻型纸

页数237页

字数1千字

定价737元

上书时间2024-12-02

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Format Paperback | 237 pages

Dimensions 155 x 235 x 13.97mm | 403g

Publication date 06 Oct 2012

Publisher Springer-Verlag New York Inc.

Language English

Edition Statement Softcover reprint of the original 1st ed. 1993

Illustrations note XVIII, 237 p.

ISBN10 1461269407

ISBN13 9781461269403

书籍简介

基于克莱蒙特麦肯纳学院的讲座，本书构成了对线性代数的实质性、抽象的介绍。演讲强调结构元素而不是计算——例如，从一开始就将矩阵连接到线性变换——并为学生进一步学习抽象数学做好准备。在这个级别的代数文本中，它是独一无二的，它在讨论的早期引入了群论，作为非正式公理系统严格发展的一个例子。

Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.

目录

1 Sets and Functions.- 1.1 Notation and Terminology.- 1.2 Composition of Functions.- 1.3 Inverse Functions.- 1.4 Digression on Cardinality.- 1.5 Permutations.- Exercises.- 2 Groups and Group Homomorphisms.- 2.1 Groups and Subgroups.- 2.2 Group Homomorphisms.- 2.3 Rings and Fields.- Exercises.- 3 Vector Spaces and Linear Transformations.- 3.1 Vector Spaces and Subspaces.- 3.2 Linear Transformations.- 3.3 Direct Products and Internal Direct Sums.- Exercises.- 4 Dimension.- 4.1 Bases and Dimension.- 4.2 Vector Spaces Are Free.- 4.3 Rank and Nullity.- Exercises.- 5 Matrices.- 5.1 Notation and Terminology.- 5.2 Introduction to Linear Systems.- 5.3 Solution Techniques.- 5.4 Multiple Systems and Matrix Inversion.- Exercises.- 6 Representation of Linear Transformations.- 6.1 The Space of Linear Transformations.- 6.2 The Representation of Hom(kn,km).- 6.3 The Representation of Hom(V,V').- 6.4 The Dual Space.- 6.5 Change of Basis.- Exercises.- 7 Inner Product Spaces.- 7.1 Real Inner Product Spaces.- 7.2 Orthogonal Bases and Orthogonal Projection.- 7.3 Complex Inner Product Spaces.- Exercises.- 8 Determinants.- 8.1 Existence and Basic Properties.- 8.2 A Nonrecursive Formula; Uniqueness.- 8.3 The Determinant of a Product; Invertibility.- Exercises.- 9 Eigenvalues and Eigenvectors.- 9.1 Definitions and Elementary Properties.- 9.2 Hermitian and Unitary Transformations.- 9.3 Spectral Decomposition.- Exercises.- 10 Triangulation and Decomposition of Endomorphisms.- 10.1 The Cayley-Hamilton Theorem.- 10.2 Triangulation of Endomorphisms.- 10.3 Decomposition by Characteristic Subspaces.- 10.4 Nilpotent Mappings and the Jordan Normal Form.- Exercises.- Supplementary Topics.- 1 Differentiation.- 2 The Determinant Revisited.- 3 Quadratic Forms.- 4 An Introduction to Categories and Functors.

作者简介

Robert J Valenza 克莱蒙特麦肯纳学院 Dengler-Dykema 数学与人文学科教授

Robert J Valenza Dengler-Dykema Professor of Mathematics and the Humanities at Claremont McKenna College

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线性代数 Linear Algebra 英文原版

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