線性代數

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

內容概要

　　《線性代數(第2版)(英文影印版)》是Kenneth Hoffman《線性代數》第2版。本版在第1版的基礎上作了一些增加和改進，尤其是在典范式和內積空間的講述上做了較大的改變。作者從線性代數的最基本知識開始講述了典范型、內積空間、雙線性型、復內積空間以及譜理論。書中許多定理的證明非常完整，受到廣大數學學者的贊賞，并且非常適合初學者學習理解。對偶空間和張量在《線性代數(第2版)(英文影印版)》同時講解，這也是《線性代數(第2版)(英文影印版)》的一大特色。

書籍目錄

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

編輯推薦

　　對于有數學功底的本科生來說，《線性代數(第2版)(英文影印版)》可以作為進入研究生學習的很好準備。

圖書封面

圖書標簽Tags

無

評論、評分、閱讀與下載

---

    線性代數 PDF格式下載

---