《線性代數》是2017年世界圖書出版公司出版的圖書，作者是[美]Peter Petersen。
基本介紹
- 中文名：線性代數
- 作者：[美]Peter Petersen
- 類別：自然科學
- 出版社：世界圖書出版公司
- 出版時間：2017年5月
- 開本：16 開
- 裝幀：平裝
- ISBN：9787519219215
內容簡介,圖書目錄,
內容簡介
《線性代數》是Undergraduate Texts in Mathematics叢書之一。內容包括大學高年級學生為升入研究生的知識，如復矢量空間，復內積，正常運算元用的譜定理，雙數空間，*小多項式，若而當典範形，有理典範形，*後一章介紹行列式。《線性代數》與同類書相比，別具特色。例如，高斯消元法被作為一個獲得特徵值得主要工具，各章有美妙的習題，等等。讀者對象：數學專業大學高年級本科生
圖書目錄
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
