高等线性代数(第3版) [Advanced Linear Algebra]

高等线性代数(第3版) [Advanced Linear Algebra] 下载 mobi epub pdf 电子书 2025


简体网页||繁体网页
[美] 罗曼 著

下载链接在页面底部
点击这里下载
    


想要找书就要到 新城书站
立刻按 ctrl+D收藏本页
你会得到大惊喜!!

发表于2025-01-18

图书介绍


出版社: 世界图书出版公司
ISBN:9787506292528
版次:1
商品编码:10096491
包装:平装
外文名称:Advanced Linear Algebra
开本:24开
出版时间:2008-08-01
用纸:胶版纸
页数:522
正文语种:英语


类似图书 点击查看全场最低价

相关图书





图书描述

内容简介

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。

内页插图

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
1 Vector 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

2 Linear 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

3 The 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

4 Modules 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

5 Modules II: Free and Noetherian Modules
The Rank of a Free Module
Free Modules and Epimorphisms
Noetherian Modules
The Hilbert Basis Theorem
Exercises

6 Modules 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

Indecomposable Modules
Exercises 159

7 The Structure of a Linear Operator
The Module Associated with a Linear Operator
The Primary Cyclic Decomposition of VT
The Characteristic Polynomial
Cyclic and Indecomposable Modules
The Big Picture
The Rational Canonical Form
Exercises

8 Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Geometric and Algebraic Multiplicities
The Jordan Canonical Form
Triangularizability and Schurs Theorem
Diagonalizable Operators
Exercises

9 Real and Complex Inner Product Spaces
Norm and Distance
Isometrics
Orthogonality
Orthogonal and Orthonormal Sets
The Projection Theorem and Best Approximations
The Riesz Representation Theorem
Exercises

10 Structure Theory for Normal Operators
The Adjoint of a Linear Operator
Orthogonal Projections
Unitary Diagonalizability
Normal Operators
Special Types of Normal Operators
Seif-Adjoint Operators
Unitary Operators and Isometries
The Structure of Normal Operators
Functional Calculus
Positive Operators
The Polar Decomposition of an Operator
Exercises

Part Ⅱ-Topics
11 Metric Vector Spaces: The Theory of Bilinear Forms
Symmetric Skew-Symmetric and Alternate Forms
The Matrix ofa Bilinear Form
Quadratic Forms
Orthogonality
Linear Functionals
Orthogonal Complements and Orthogonal Direct Sums
Isometrics
Hyperbolic Spaces
Nonsingular Completions ofa Subspace
The Witt Theorems: A Preview
The Classification Problem for Metric Vector Spaces
Symplectic Geometry
The Structure of Orthogonal Geometries: Orthogonal Bases
The Classification of Orthogonal Geometries:Canonical Forms
The Orthogonal Group
The Witt Theorems for Orthogonal Geometries
Maximal Hyperbolic Subspaces of an Orthogonal Geometry
Exercises

12 Metric Spaces
The Definition
Open and Closed Sets
Convergence in a Metric Space
The Closure of a Set
Dense Subsets
Continuity
Completeness
Isometrics
The Completion of a Metric Space
Exercises

13 Hilbert Spaces
A Brief Review
Hilbert Spaces
Infinite Series
An Approximation Problem
Hilbert Bases
Fourier Expansions
A Characterization of Hilbert Bases
Hilbert Dimension
A Characterization of Hilbert Spaces
The Riesz Representation Theorem
Exercises

14 Tensor Products
Universality
Bilinear Maps
Tensor Products
When Is a Tensor Product Zero?
Coordinate Matrices and Rank
Characterizing Vectors in a Tensor Product
Defining Linear Transformations on a Tensor Product
The Tensor Product of Linear Transformations
Change of Base Field
Multilinear Maps and Iterated Tensor Products
Tensor Spaces
Special Multilinear Maps
Graded Algebras
The Symmetric and Antisymmetric Tensor Algebras
The Determinant
Exercises

15 Positive Solutions to Linear Systems:Convexity and Separation
Convex Closed and Compact Sets
Convex Hulls
Linear and Affine Hyperplanes
Separation
Exercises

16 Affine Geometry
Affine Geometry
Affine Combinations
Affine Hulls
The Lattice of Flats
Affine Independence
Affine Transformations
Projective Geometry
Exercises

17 Singular Values and the Moore-Penrose Inverse
Singular Values
The Moore-Penrose Generalized Inverse
Least Squares Approximation
Exercises

18 An Introduction to Algebras
Motivation
Associative Algebras
Division Algebras
Exercises

19 The Umbral Calculus
Formal Power Series
The Umbral Algebra
Formal Power Series as Linear Operators
Sheffer Sequences
Examples of Sheffer Sequences
Umbral Operators and Umbral Shifts
Continuous Operators on the Umbral Algebra
Operator Adjoints
Umbral Operators and Automorphisms of the Umbral Algebra
Umbral Shifts and Derivations of the Umbral Algebra
The Transfer Formulas
A Final Remark
Exercises
References
Index of Symbols
Index

前言/序言

  Let me begin by thanking the readers of the second edition for their many helpful comments and suggestions, with special thanks to Joe Kidd and Nam Trang. For the third edition, I have corrected all known errors, polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products) and upgraded some proofs that were originally done only for finite-dimensional/rank cases. I have also moved some of the material on projection operators to an earlier oosition in the text.

高等线性代数(第3版) [Advanced Linear Algebra] 下载 mobi epub pdf txt 电子书 格式

高等线性代数(第3版) [Advanced Linear Algebra] mobi 下载 pdf 下载 pub 下载 txt 电子书 下载 2025

高等线性代数(第3版) [Advanced Linear Algebra] 下载 mobi pdf epub txt 电子书 格式 2025

高等线性代数(第3版) [Advanced Linear Algebra] 下载 mobi epub pdf 电子书
想要找书就要到 新城书站
立刻按 ctrl+D收藏本页
你会得到大惊喜!!

用户评价

评分

快!真是快!

评分

此用户未填写评价内容

评分

书本质量还可以,内容有点深,看得吃力

评分

( ^_^ )不错嘛,纸质可以,物流也给力

评分

中国人民大学经济学院最早成立于1988年,由著名经济学家黄达任首任院长。1998年经济学院进行了调整,下设经济学系、国际经济系、经济研究所以及中国改革与发展研究院。中国人民大学经济学院的前身可以追溯到1951年创办的中国人民大学经济学系。建国初期,经济学系曾为我国培养了大批马克思主义经济理论人才和经济工作者,更重要的是,在改革开放时期,为推进社会主义市场经济理论做出了积极的贡献。经济学院重建以后,在理论创新、教学改革、队伍建设等方面都取得了辉煌的成就。1991-1998年,经济学院共承担国家社会科学基金科研项目55项,获得国家和省部级科研奖31项。1998年,经过严格评审,中国人民大学经济学院被教育部确定为国家经济学理论人才培养基地。

评分

这本书算是经典了,过段时间再看

评分

( ^_^ )不错嘛,纸质可以,物流也给力

评分

评分

Part 2: Algebraic Structures

类似图书 点击查看全场最低价

高等线性代数(第3版) [Advanced Linear Algebra] mobi epub pdf txt 电子书 格式下载 2025


分享链接




相关图书


本站所有内容均为互联网搜索引擎提供的公开搜索信息,本站不存储任何数据与内容,任何内容与数据均与本站无关,如有需要请联系相关搜索引擎包括但不限于百度google,bing,sogou

友情链接

© 2025 book.cndgn.com All Rights Reserved. 新城书站 版权所有