深度学习数学基础介绍（一）线性代数

推荐MIT的线代课程：

 

1 The geometry of linear equations
线性代数的几何意义
2 Elimination with matrices
矩阵消元
3 Matrix operations and inverses
乘法和逆矩阵
4 LUand LDU factorization
A的LU分解
5 Transposes and permutations Problem set 1 due
转置-置换-向量空间R
6 Vector spaces and subspaces
列空间和零空间
7 The nullspace: Solving Ax = 0
求解Ax=0：主变量、特解
8 Rectangular PA = LU and Ax = b Problem set 2 due
求解Ax=b：可解性和解的结构
9 Row reduced echelon form
线性相关性、基、维数
10 Basis and dimension
四个基本子空间
11 The four fundamental subspaces Problem set 3 due
12 Exam 1: Chapters 1 to 3.4
13 Graphs and networks
14 Orthogonality Problem set 4 due
15 Projections and subspaces
16 Least squares approximations
17 Gram-Schmidt and A = QR Problem set 5 due
18 Properties of determinants
19 Formulas for determinants
20 Applications of determinants Problem set 6 due
21 Eigenvalues and eigenvectors
22 Diagonalization
23 Markov matrices Problem set 7 due
24 Review for exam 2
25 Exam 2: Chapters 1-5, 6.1-6.2, 8.2
26 Differential equations
27 Symmetric matrices
28 Positive definite matrices
29 Matrices in engineering Problem set 8 due
30 Similar matrices
31 Singular value decomposition Problem set 9 due
32 Fourier series, FFT, complex matrices
33 Linear transformations
34 Choice of basis Problem set 10 due
35 Linear programming
36 Course review
37 Exam 3: Chapters 1-8 (8.1, 2, 3, 5)
38 Numerical linear algebra
39 Computational science
40 Final exam