高等线性代数(第3版)(英文版)

本书是Springer《数学研 究生教材》第135卷。全书 分为两部分，第一部分主要 阐述线性代数基本理论，第 二部分对九个专题做了讨论 。目次：（一）线性代数基 本理论：矢量空间；线性变 换；同构定理；模；通过理 想整环建立的模，线性算子 结构；特征值和特征向量； 实与复内积空间；谱定理用 于正规算子。（二）专题： 度量向量空间；度量空间， 希耳伯特空间；张量乘积仿 射几何学；哑运算。本书读 者对象为数学及有关专业高 年级大学生和研究生。

Preface to the Third Edition Preface to the Second Edition Preface to the First Edition 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 Complexification 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