线性代数

前言

　　Our original purpose in writing this book was to provide a text for the undergraduate linear algebra course at the Massachusetts Institute of Technology. This course was designed for mathematics majors at the junior level， although threefourths of the stu

书籍目录

Chapter 1.　Linear Equations1.1.　Fields1.2.　Systems of Linear Equations1.3.　Matrices and Elementary Row Operations1.4.　Row-Reduced Echelon Matrices1.5.　Matrix Multiplication1.6.　Invertible MatricesChapter 2.　Vector Spaces2.1.　Vector Spaces2.2.　Subspaces2.3.　Bases and Dimension2.4.　Coordinates2.5.　Summary of Row-Equivalence2.6.　Computations Concerning SubspacesChapter 3.　Linear Transformations3.1.　Linear Transformations3.2.　The Algebra of Linear Transformations3.3.　Isomorphism3.4.　Representation of Transformations by Matrices3.5.　Linear Functionals3.6.　The Double Dual3.7.　The Transpose of a Linear TransformationChapter 4.　Polynomials4.1.　Algebras4.2.　The Algebra of Polynomials4.3.　Lagrange Interpolation4.4.　Polynomial Ideals4.5.　The Prime Factorization of a PolynomialChapter 5.　Determinants5.1.　Commutative Rings5.2.　Determinant Functions5.3.　Permutations and the Uniqueness of Determinants5.4.　Additional Properties of Determinants5.5.　Modules5.6.　Multilinear Functions5.7.　The Grassman RingChapter 6.　Elementary Canonical Forms6.1.　Introduction6.2.　Characteristic Values6.3.　.Annihilating Polynomials6.4.　Invariant Subspaces6.5.　simultaneous Triangulation; Simultaneous Diagonalization6.6.　Direct-Sum Decompositions6.7.　Invarlant Direct Sums6.8.　The Primary Decomposition TheoremChapter 7.　The Rational and Jordan Forms7.1.　Cyclic Subspaces and Annihilators7.2.　Cyclic Decompositions and the Rational Form7.3.　The Jordan Form7.4.　Computation of Invarlant Factors7.5.　Summary; Semi-Simple OperatorsChapter 8.　Inner Product Spaces8.1.　Inner Products8.2.　Inner Product Spaces8.3.　Linear Functional] and Adjoints8.4.　Unitary Operators8.5.　Normal OperatorsChapter 9.　Operators on Inner Product Spaces9.1. Introduction9.2.　Forms on Inner Product Spaces9.3. Positive Forms9.4. More on Forms9.5. Spectral Theory9.6. Further Properties of Normal OperatorsChapter 10. Bilinear Forms10.1.　Bilinear Forms10.2.　Symmetric Bilinear Forms10.3.　Skew-SymmetricBilinear Forms10.4　Groups Preserving Bilinear FormsAppendixA.1.　SetsA.2. FunctionsA.3. Equivalence RelationsA.4.　Quotient SpacesA.5.　Equivalence Relations in Linear AlgebraA.6.　The Axiom of ChoiceBibliographylndes

编辑推荐

　　对于有数学功底的本科生来说，《线性代数(第2版)(英文影印版)》可以作为进入研究生学习的很好准备。

作者简介

《线性代数(第2版)(英文影印版)》是Kenneth Hoffman《线性代数》第2版。本版在第1版的基础上作了一些增加和改进,尤其是在典范式和内积空间的讲述上做了较大的改变。作者从线性代数的最基本知识开始讲述了典范型、内积空间、双线性型、复内积空间以及谱理论。书中许多定理的证明非常完整，受到广大数学学者的赞赏，并且非常适合初学者学习理解。对偶空间和张量在《线性代数(第2版)(英文影印版)》同时讲解，这也是《线性代数(第2版)(英文影印版)》的一大特色。

图书封面

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