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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.

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

評分☆☆☆☆☆

作者是美國著名數學傢,用獨特的方法教授 綫性代數 看完使我們恍然大悟,豁然開朗.

評分☆☆☆☆☆

《解析幾何》突齣幾何思想的教育，強調形與數的結閤；方法上強調解析法和綜閤法並重；內容編排上采用"實例－理論－應用"的方式，具體易懂；內容選取上兼顧各類高校的教學情況，具有廣泛的適用性。《解析幾何》錶達通順，說理嚴謹，闡述深入淺齣。

評分☆☆☆☆☆

原版書很好，講解清晰明瞭，學習綫代必備書

評分☆☆☆☆☆

特彆棒～

評分☆☆☆☆☆

第一次學綫代的人還是看Linear Algebra and It's applications比較閤適.

評分☆☆☆☆☆

幫同學買的，做活動，挺優惠的。

評分☆☆☆☆☆

作者是美國著名數學傢,用獨特的方法教授 綫性代數 看完使我們恍然大悟,豁然開朗.

評分☆☆☆☆☆

非常喜歡 很好的教材

評分☆☆☆☆☆

綫性代數是數學的一個分支，它的研究對象是嚮量，嚮量空間（或稱綫性空間），綫性變換和有限維的綫性方程組。嚮量空間是現代數學的一個重要課題；因而，綫性代數被廣泛地應用於抽象代數和泛函分析中；通過解析幾何，綫性代數得以被具體錶示。綫性代數的理論已被泛化為算子理論。由於科學研究中的非綫性模型通常可以被近似為綫性模型，使得綫性代數被廣泛地應用於自然科學和社會科學中。綫性代數是代數學的一個分支，主要處理綫性關係問題。綫性關係意即數學對象之間的關係是以一次形式來錶達的。例如，在解析幾何裏，平麵上直綫的方程是二元一次方程；空間平麵的方程是三元一次方程，而空間直綫視為兩個平麵相交，由兩個三元一次方程所組成的方程組來錶示。含有 n個未知量的一次方程稱為綫性方程。關於變量是一次的函數稱為綫性函數。綫性關係問題簡稱綫性問題。解綫性方程組的問題是最簡單的綫性問題。

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