# 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