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店鋪：暗香盈袖圖書專營店

齣版社：浙江大學齣版社

ISBN：7308038300

商品編碼：26493748003

叢書名：綫性代數

開本：26開

齣版時間：2004-08-01

具體描述

Linear Algebra Done Right 2nd ed

綫性代數

第2版英文版

作者：（美）阿剋斯勒（Axler，S.）Sheldon Axler 著

齣版社：世界圖書齣版公司

齣版時間：2008-5-1

版次：1
頁數：251
字數：
印刷時間：2008-5-1
開本：16開
紙張：膠版紙
印次：1
I S B N：9787506292191
包裝：平裝
定價：49.00元

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.

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