线性代数（第2版）（英文影印版） [LINEAR ALGEBRA DONE RIGHT 2nd ed] 下载 mobi epub pdf 电子书 2024

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内容简介

　　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.

内页插图

目录

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.

线性代数（第2版）（英文影印版） [LINEAR ALGEBRA DONE RIGHT 2nd ed] 下载 mobi epub pdf txt 电子书 格式

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《线性代数（第2版）》为高等院校理工科教材，全书共7章，内容包括：行列式；矩阵；线性方程组；向量空间与线性变换；特征值和特征向量，矩阵的对角化；二次型及应用问题，书末附录中还介绍了内积空间，埃尔米特二次型；约当（Jordan）标准形；并汇编了历年硕士研究生入学考试中的线生代数试题。本书内容丰富，层次清晰，阐述深入浅出，简明扼要，可作为高等院校的教材（适用于35-70课的教学）或教学参考书和考研复习用书。《线性代数（数学专业用）》是普通高等教育“十五”国家级规划教材，是作者主讲的国家级精品课程“线性代数”所使用的教材。适合作为大学本科数学类专业线性代数（或称“高等代数”）课程的教材，也可作为各类大专院校师生的参考书，以及关心线性代数和矩阵论知识的科技工作者或其他读者的自学读物或参考书。

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好书，正版。赞京东，还来

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很难得，很清楚，很好。

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