2.C Dimension
第二章 有限维向量空间 (4 小时)
2.A 张成空间与线性无关
2.B 基
2.C 维数
Chapter 3 Linear Maps (10 hours)
3.A The Vector Space of Linear Maps: Definitions and Examples of Linear Maps, Algebraic Operations on L(V,W).
3.B Null Spaces and Ranges: Null Space and Injectivity, Range and Surjectivity, Fundamental Theorem of Linear Maps.
3.C Matrices: Representing a Linear Map by a Matrix, Addition and Scalar Multiplication of Matrices, Matrix Multiplication.
3.D Invertibility and Isomorphic Vector Spaces: Invertible Linear Maps, Isomorphic Vector Spaces, Linear Maps Thought
of as Matrix Multiplication, Operators.
3.E Products and Quotients of Vector Spaces: Products of Vector Spaces, Products and Direct Sums, Quotients of
Vector Spaces.
3.F Duality; The Dual Space and the Dual Map, The Null Space and Range of the Dual of a Linear Map, The Matrix of
the Dual of a Linear Map, The Rank of a Matrix.
第三章 线性映射 (10 小时)
3.A 向量空间的线性映射
3.B 零空间与值域
3.C 矩阵
3.D 可逆性与同构的向量空间
3.E 向量空间的积与商
3.F 对偶
Chapter 4 Polynomials (4 hours)
Complex Conjugate and Absolute Value, Uniqueness of Coefficients for Polynomials, The Division Algorithm for
Polynomials, Zeros of Polynomials, Factorization of Polynomials over C, Factorization of Polynomials over R.
第四章 多项式 (4 小时)
Chapter 5 Eigenvalues, Eigenvectors, and Invariant Subspaces (6 hours)
5.A Invariant Subspaces: Eigenvalues and Eigenvectors, Restriction and Quotient Operators.
5.B Eigenvectors and Upper-Triangular Matrices: Polynomials Applied to Operators, Existence of Eigenvalues, Upper-
Triangular Matrices.
5.C Eigenspaces and Diagonal Matrices
第五章 本征值、本征向量、不变子空间 (6 小时)
5.A 不变子空间
5.B 本征向量与上三角矩阵
5.C 本征空间与对角矩阵
Chapter 6 Inner Product Spaces (6 hours)
6.A Inner Products and Norms: Inner Products, Norms.
6.B Orthonormal Bases: Linear Functionals on Inner Product Spaces.
6.C Orthogonal Complements and Minimization Problems: Orthogonal Complements, Minimization Problems.
第六章 内积空间 (6 小时)