0. 목차

Original Source: https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/

Linear Algebra | Mathematics | MIT OpenCourseWare

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Ⅰ. $ A \mathbf{x} = \mathbf{b} $ and the Four Subspaces

1. The Geometry of Linear Equations
2. Elimination with Matrices
3. Multiplication and Inverse Matrices
4. Factorization into $ A = LU $
5. Transposes, Permutations, Vector Spaces
6. Column Space and Nullspace
7. Solving $ A \mathbf{x} = \mathbf{0} $; Pivot Variables, Special Solutions
8. Solving $ A \mathbf{x} = \mathbf{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

Ⅱ. Least Squares, Determinants and Eigenvalues

1. Orthogonal Vectors and Subspaces
2. Projections onto Subspaces
3. Projection Matrices and Least Squares
4. Orthogonal Matrices and Gram-Schmidt
5. Properties of Determinants
6. Determinant Formulas and Cofactors
7. Cramer's Rule, Inverse Matrix and Volume
8. Eigenvalues and Eigenvectors
9. Diagonalization and Powers of $ A $
10. Differential Equations and $ \exp(At) $
11. Markov Matrices; Fourier Series

Ⅲ. Positive Definite Matrices and Applications

1. Symmetric Matrices and Positive Definiteness
2. Complex Matrices; Fast Fourier Transform
3. Positive Definite Matrices and Minima
4. Similar Matrices and Jordan Form
5. Singular Value Decomposition
6. Linear Transformations and Their Matrices
7. Change of Basis; Image Compression
8. Left and Right Inverses; PseudoInverse