商品簡介
《線性代數》(第2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)同時講解，這也是《線性代數》(第2版)的一大特色。
目次
Chapter 1.Linear Equations
1.1.Fields
1.2.Systems of Linear Equations
1.3.Matrices and Elementary Row Operations
1.4.Row-Reduced Echelon Matrices
1.5.Matrix Multiplication
1.6.Invertible Matrices
Chapter 2.Vector Spaces
2.1.Vector Spaces
2.2.Subspaces
2.3.Bases and Dimension
2.4.Coordinates
2.5.Summary of Row-Equivalence
2.6.Computations Concerning Subspaces
Chapter 3.Linear Transformations
3.1.Linear Transformations
3.2.The Algebra of Linear Transformations
3.3.Isomorphism
3.4.Representation of Transformations by Matrices
3.5.Linear Functionals
3.6.The Double Dual
3.7.The Transpose of a Linear Transformation
Chapter 4.Polynomials
4.1.Algebras
4.2.The Algebra of Polynomials
4.3.Lagrange Interpolation
4.4.Polynomial Ideals
4.5.The Prime Factorization of a Polynomial
Chapter 5.Determinants
5.1.Commutative Rings
5.2.Determinant Functions
5.3.Permutations and the Uniqueness of Determinants
5.4.Additional Properties of Determinants
5.5.Modules
5.6.Multilinear Functions
5.7.The Grassman Ring
Chapter 6.Elementary Canonical Forms
6.1.Introduction
6.2.Characteristic Values
6.3.Annihilating Polynomials
6.4.Invariant Subspaces
6.5.Simultaneous Triangulation; Simultaneous Diagonalization
6.6.Direct-Sum Decompositions
6.7.Invariant Direct Sums
6.8.The Primary Decomposition Theorem
Chapter 7.The Rational and Jordan Forms
7.1.Cyclic Subspaces and Annihilators
7.2.Cyclic Decompositions and the Rational Form
7.3.The Jordan Form
7.4.Computation of Invariant Factors
7.5.Summary; Semi-Simple Operators
Chapter 8.Inner Product Spaces
8.1.Inner Products
8.2.Inner Product Spaces
8.3.Linear Functionals and Adjoints
8.4.Unitary Operators
8.5.Normal Operators
Chapter 9.Operators on Inner Product Spaces
Chapter 10.Bilinear Forms
Appendix
Biblioaphy
Index
