綫性代數（第2版）（英文影印版） [LINEAR ALGEBRA DONE RIGHT 2nd ed] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

[美] 阿剋斯勒（Axler，S.） 著

齣版社： 世界圖書齣版公司北京公司

ISBN：9787506292191

版次：1

商品編碼：10096471

包裝：平裝

外文名稱：LINEAR ALGEBRA DONE RIGHT 2nd ed

開本：16開

齣版時間：2008-05-01

用紙：膠版紙

頁數：251

正文語種：英語

內容簡介

　　The audacious title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue. Determinants are difficult, nonintuitive, and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces, most books must.define determinants, prove that a linear map is not invertible ff and only if its determinant equals O, and then define the characteristic polynomial. This tortuous (torturous?) path gives students little feeling for why eigenvalues must exist. In contrast, the simple determinant-free proofs presented here offer more insight. Once determinants have been banished to the end of the book, a new route opens to the main goal of linear algebra-- understanding the structure of linear operators.

內頁插圖

目錄

Preface to the Instructor
Preface to the Student
Acknowledgments
CHAPTER 1
Vector Spaces
Complex Numbers
Definition of Vector Space
Properties of Vector Spaces
Subspaces
Sums and Direct Sums
Exercises

CHAPTER 2
Finite-Dimenslonal Vector Spaces
Span and Linear Independence
Bases
Dimension
Exercises

CHAPTER 3
Linear Maps
Definitions and Examples
Null Spaces and Ranges
The Matrix of a Linear Map
Invertibility
Exercises

CHAPTER 4
Potynomiags
Degree
Complex Coefficients
Real Coefflcients
Exercises

CHAPTER 5
Eigenvalues and Eigenvectors
lnvariant Subspaces
Polynomials Applied to Operators
Upper-Triangular Matrices
Diagonal Matrices
Invariant Subspaces on Real Vector Spaces
Exercises

CHAPTER 6
Inner-Product spaces
Inner Products
Norms
Orthonormal Bases
Orthogonal Projections and Minimization Problems
Linear Functionals and Adjoints
Exercises

CHAPTER 7
Operators on Inner-Product Spaces
Self-Adjoint and Normal Operators
The Spectral Theorem

Normal Operators on Real Inner-Product Spaces
Positive Operators
Isometries
Polar and Singular-Value Decompositions
Exercises

CHAPTER 8
Operators on Complex Vector Spaces
Generalized Eigenvectors
The Characteristic Polynomial
Decomposition of an Operator
Square Roots
The Minimal Polynomial
Jordan Form
Exercises

CHAPTER 9
Operators on Real Vector Spaces
Eigenvalues of Square Matrices
Block Upper-Triangular Matrices
The Characteristic Polynomial
Exercises

CHAPTER 10
Trace and Determinant
Change of Basis
Trace
Determinant of an Operator
Determinant of a Matrix
Volume
Exercises
Symbol Index
Index

前言/序言

　　You are probably about to teach a course that will give students their second exposure to linear algebra. During their first brush with the subject， your students probably worked with Euclidean spaces and matrices. In contrast， this course will emphasize abstract vector spaces and linear maps.
　　The audacious title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue.Determinants are difficult， nonintuitive， and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces， most books must define determinants， prove that a linear map is not invertible if and only ff its determinant equals O， and then define the characteristic polynomial. This tortuous （torturous？） path gives students little feeling for why eigenvalues must exist.
　　In contrast， the simple determinant-free proofs presented here offer more insight. Once determinants have been banished to the end of the book， a new route opens to the main goal of linear algebra-understanding the structure of linear operators.
　　This book starts at the beginning of the subject， with no prerequi-sites other than the usual demand for suitable mathematical maturity.Even if your students have already seen some of the material in the first few chapters， they may be unaccustomed to working exercises of the type presented here， most of which require an understanding of proofs.
　　Vector spaces are defined in Chapter 1， and their basic propertiesare developed.

評分☆☆☆☆☆

好評如潮流言論壇蜜時代背景音樂會

評分☆☆☆☆☆

2．“空間為體，矩陣為用”，自始至終強調幾何與代數的相互滲透。

評分☆☆☆☆☆

非常好的一本綫性代數自學教材

評分☆☆☆☆☆

還不錯，搞活動買的，價格閤適

評分☆☆☆☆☆

書很經典，很適閤係統地學習綫性代數。

評分☆☆☆☆☆

書的體係寫的不錯，學習高代更容易理解

評分☆☆☆☆☆

很不錯，還沒看過但是包裝不錯

評分☆☆☆☆☆

不錯的書，看得很纍。

評分☆☆☆☆☆

美國最受歡迎最好的綫性代數教材! 各章節條理清晰,概念定義、定理證明嚴謹,並且闡述動機。 課後習題難度適中,主要是加深對本章內容的理解,不是教你怎麼計算的。 隻要仔細讀完本章,習題基本都能做。此書錶明瞭作者認為綫性代數該這麼講,對於想加深理解綫性代數的,此書正是你想要的。