高等线性代数 第3版
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作者： （美）罗曼著
出 版 社： 世界图书出版公司
出版时间： 2008-8-1字数：版次： 1页数： 522印刷时间： 2008-08-01开本： 24开印次： 1纸张： 胶版纸I S B N ： 9787506292528包装： 平装内容简介
This book is a thorough introduction to linear algebra，for the graduate or advanced undergraduate student。 Prerequisites are limited to a knowledge of the basic properties of matrices and determinants。 However，since we cover the basics of vector spaces and linear transformations rather rapidly，a prior course in linear algebra （even at the sophomore level），along with a certain measure of "mathematical maturity," is highly desirable。
目录
Preface to the Third Edition，vii
Preface to the Second Edition，ix
Preface to the First Edition，xi
Preliminaries
Part 1: Preliminaries
Part 2: Algebraic Structures
Part I Basic Linear Algebra
1Vector Spaces
Vector Spaces
Subspaces
Direct Sums
Spanning Sets and Linear Independence
The Dimension of a Vector Space
Ordered Bases and Coordinate Matrices
The Row and Column Spaces of a Matrix
The C0mplexification of a Real Vector Space
Exercises
2Linear Transformations
Linear Transformations
The Kernel and Image of a Linear Transformation
Isomorphisms
The Rank Plus Nullity Theorem
Linear Transformations from Fn to Fm
Change of Basis Matrices
The Matrix of a Linear Transformation
Change of Bases for Linear Transformations
Equivalence of Matrices
Similarity of Matrices
Similarity of Operators
Invariant Subspaces and Reducing Pairs
Projection Operators
Topological Vector Spaces
Linear Operators on Vc
Exercises
3The Isomorphism Theorems
Quotient Spaces
The Universal Property of Quotients and the First Isomorphism Theorem
Quotient Spaces，Complements and Codimension
Additional Isomorphism Theorems
Linear Functionals
Dual Bases
Reflexivity
Annihilators
Operator Adjoints
Exercises
4Modules I: Basic Properties
Motivation
Modules
Submodules
Spanning Sets
Linear Independence
Torsion Elements
Annihilators
Free Modules
Homomorphisms
Quotient Modules
The Correspondence and Isomorphism Theorems
Direct Sums and Direct Summands
Modules Are Not as Nice as Vector Spaces
Exercises
5Modules II: Free and Noetherian Modules
The Rank of a Free Module
Free Modules and Epimorphisms
Noetherian Modules
The Hilbert Basis Theorem
Exercises
6Modules over a Principal Ideal Domain
Annihilators and Orders
Cyclic Modules
Free Modules over a Principal Ideal Domain
Torsion-Free and Free Modules
The Primary Cyclic Decomposition Theorem
The Invariant Factor Decomposition
Characterizing Cyclic Modules
lndecomposable Modules
Exercises
7The Structure of a Linear Operator
8Eigenvalues and Eigenvectors
9Real and Complex Inner Product Spaces
10 Structure Theory for Normal Operators
Part ll--Topics
11 Metric Vector Spaces: The Theory of Bilinear Forms
12 Metric Spaces
13 Hilbert Spaces
14 Tensor Products
15 Positive Solutions to Linear Systems:Convexity and Separation
16 Affine Geometry
17 Singular Values and the Moore-Penrose Inverse
18 An Introduction to Algebras
19 The Umbral Calculus
Referenees
Index of Symbols
Index
