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Math 220: Linear Algebra


Spring 2010

Contents [Top]

Procedural Documents  [Top Contents]

About Linear Algebra

  • A brief history of linear algebra (here)
  • Pronunciation guide (here)

Topics of Study  [Top Contents]

Topic Handouts Lectures Notes Reading guides
Chapter 1: Matrices and Systems of Linear Equations Matlab .m files iterate and transformations 1.0 notes
1.1 notes
1.2 notes
1.3 notes
1.4 notes
1.5 notes
1.6 notes
1.7 notes
1.8 was skipped
1.9 notes 		 
Chapter 3: Vector Space in R^3   3.1 notes
3.2 notes
3.3 notes
3.4 notes
3.5 notes
3.6 notes
3.7 notes
3.8 notes
3.9 notes		  
Chapter 4: The Eigenvalue Problem   4.1 notes
4.2 notes
4.3 was skipped
4.4 notes
4.5 notes
4.6 notes
4.7 notes		  

 

Study Guides, Tests and Test Keys  [Top  Contents]

Topic Review Test

Test Key
Quiz 1   Quiz Key
Test 1 Review notes Test Key
Quiz 2   Quiz Key
Quiz 3   Quiz Key
Test 2   Test Key
Test 3 Test Key
Final Exam      

Videos  [Top Contents]

Additional supplemental materials (including these video lectures) may be found on the MIT OpenCourseWare site

Lecture Topic
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