Linear algebra : a pure mathematical approach线性代数
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作者： Harvey E. Rose著
出 版 社：
出版时间： 2002-10-1字数：版次： 1页数： 250印刷时间： 2002/10/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783764367923包装： 平装编辑推荐
作者简介：
"Rose's Linear Algebra is a highly sophisticated undergraduate work...This book would be excellent for mathematics majors or for non-majors with access to a second course in which applications were presented. Summing Up: Recommended for lower- and upper-division undergraduates."
内容简介
Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach.
A large number of examples, exercises and problems are provided. Answers and/or sketch solutions to all of the problems are given in an appendix. The intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a "second course" in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, the book can be used for a "first course" for more advanced students.
目录
Preface
Chapter 1 Algebraic Preamble
Groups, Rings and Fields
Permutation Groups
Problems 1
Chapter 2 Vector Spaces and Linear Maps
Vector Spaces and Algebras
Bases and Dimension
Linear Maps
Direct Sums
Addendum -- Modules
Problems 2
Chapter 3 Matrices, Determinants and Linear Equations
Matrices
Determinants
Systems of Linear Equations
Problems 3
Chapter 4 Cayley--Hamilton Theorem and Jordan Form
Polynomials
Cayley-Hamilton and Spectral Theorems
Jordan Form
Problems 4
Chapter 5 Interlude on Finite Fields
Finite Fields
Applications-Linear Codes and Finite Matrix Groups
Problems 5
Chapter 6 Hermitian and Inner Product Spaces
Hermitian and Inner Products, and Norms
Unitary and Self-adjoint Maps
Orthogonal and Symmetric Maps
Problems 6
Chapter 7 Selected Topics
The Geometry of Real Quadratic Forms
Normed Algebras, Quaternions and Cayley Numbers
Introduction to the Representation of Finite Groups
Problems 7
Appendix A --- Set Theory 195 (10)
Sets and Maps
Problems A
Appendix B --- Answers and Solutions to the Problems 205 (34)
Bibliography
Index
Notation Index
Definition Index
Theorem Index
Subject Index
