MIT 18.06SC Linear Algebra Recitations, Fall 2011
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. Created by MIT OpenCourseWare.
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1: Course Introduction
2: Geometry of Linear Algebra
3: An Overview of Key Ideas
4: Elimination with Matrices
5: Inverse Matrices
6: LU Decomposition
7: Subspaces of Three Dimensional Space
8: Vector Subspaces
9: Solving Ax=0
10: Solving Ax=b
11: Basis and Dimension
12: Computing the Four Fundamental Subspaces
13: Matrix Spaces
14: Exam #1 Problem Solving
15: Graphs and Networks
16: Orthogonal Vectors and Subspaces
17: Projection into Subspaces
18: Least Squares Approximation
19: Gram-Schmidt Orthogonalization
20: Properties of Determinants
21: Determinants
22: Determinants and Volume
23: Eigenvalues and Eigenvectors
24: Powers of a Matrix
25: Differential Equations and exp (At)
26: Markov Matrices
27: Exam #2 Problem Solving
28: Symmetric Matrices and Positive Definiteness
29: Complex Matrices
30: Positive Definite Matrices and Minima
31: Similar Matrices
32: Computing the Singular Value Decomposition
33: Linear Transformations
34: Change of Basis
35: Pseudoinverses
36: Exam #3 Problem Solving
37: Final Exam Problem Solving