線性代數 (MIT 18.06)

MIT 18.06 Linear Algebra, Fall 1997 （麻省理工學院 Gilbert Strang 教授主講）

課程內容：

1	The Geometry of Linear Equations
2	Elimination with Matrices
3	Multiplication and Inverse Matrices
4	Factorization into A = LU
5	Transposes, Permutations, Spaces R^n
6	Column Space and Nullspace
7	Solving Ax = 0: Pivot Variables, Special Solutions
8	Solving Ax = b: Row Reduced Form R
9	Independence, Basis, and Dimension
10	The Four Fundamental Subspaces
11	Matrix Spaces; Rank 1; Small World Graphs
12	Graphs, Networks, Incidence Matrices
13	Quiz 1 Review
14	Orthogonal Vectors and Subspaces
15	Projections onto Subspaces
16	Projection Matrices and Least Squares
17	Orthogonal Matrices and Gram-Schmidt
18	Properties of Determinants
19	Determinant Formulas and Cofactors
20	Cramer's Rule, Inverse Matrix, and Volume
21	Eigenvalues and Eigenvectors
22	Diagonalization and Powers of A
23	Differential Equations and exp(At)
24	Markov Matrices; Fourier Series
24b	Quiz 2 Review
25	Symmetric Matrices and Positive Definiteness
26	Complex Matrices; Fast Fourier Transform
27	Positive Definite Matrices and Minima
28	Similar Matrices and Jordan Form
29	Singular Value Decomposition
30	Linear Transformations and Their Matrices
31	Change of Basis; Image Compression
32	Quiz 3 Review
33	Left and Right Inverses; Pseudoinverse
34	Final Course Review

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