MIT 18.06 线性代数
本笔记按章节拆分为子页，逐章阅读更快。
麻省理工 MIT 18.06 Linear Algebra（Gilbert Strang）系统学习笔记，涵盖矩阵消元与 LU 分解、向量空间与四个基本子空间、正交与最小二乘、特征值与对角化、正定矩阵与奇异值分解。
章节
- 开篇与课程概览
- Lecture 1: The Geometry of Linear Equations
- Lecture 2: Elimination with Matrices
- Lecture 3: Multiplication and Inverse Matrices
- Lecture 4: Factorization into A = LU
- Lecture 5: Transposes, Permutations, Spaces R^n
- Lecture 6: Column Space and Nullspace
- Lecture 7: Solving Ax = 0: Pivot Variables, Special Solutions
- Lecture 8: Solving Ax = b: Row Reduced Form R
- Lecture 9: Independence, Basis, and Dimension
- Lecture 10: The Four Fundamental Subspaces
- Lecture 11: Matrix Spaces; Rank 1; Small World Graphs
- Lecture 12: Graphs, Networks, Incidence Matrices
- Lecture 14: Orthogonal Vectors and Subspaces
- Lecture 15: Projections onto Subspaces
- Lecture 16: Projection Matrices and Least Squares
- Lecture 17: Orthogonal Matrices and Gram-Schmidt
- Lecture 18: Properties of Determinants
- Lecture 19: Determinant Formulas and Cofactors
- Lecture 20: Cramer’s Rule, Inverse Matrix, and Volume
- Lecture 21: Eigenvalues and Eigenvectors
- Lecture 22: Diagonalization and Powers of A
- Lecture 23: Differential Equations and exp(At)
- Lecture 24: Markov Matrices; Fourier Series
- Lecture 25: Symmetric Matrices and Positive Definiteness
- Lecture 27: Positive Definite Matrices and Minima
- Lecture 28: Similar Matrices and Jordan Form
- Lecture 29: Singular Value Decomposition
- Lecture 30: Linear Transformations and Their Matrices
- Lecture 31: Change of Basis; Image Compression
- Lecture 33: Left and Right Inverses; Pseudoinverse
- 矩阵分解速查表