Overview
Syllabus
An Interview with Gilbert Strang on Teaching Linear Algebra.
Course Introduction | MIT 18.06SC Linear Algebra.
1. The Geometry of Linear Equations.
Geometry of Linear Algebra.
Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008.
An Overview of Key Ideas.
2. Elimination with Matrices..
Elimination with Matrices.
3. Multiplication and Inverse Matrices.
Inverse Matrices.
4. Factorization into A = LU.
LU Decomposition.
5. Transposes, Permutations, Spaces R^n.
Subspaces of Three Dimensional Space.
6. Column Space and Nullspace.
Vector Subspaces.
7. Solving Ax = 0: Pivot Variables, Special Solutions.
Solving Ax=0.
8. Solving Ax = b: Row Reduced Form R.
Solving Ax=b.
9. Independence, Basis, and Dimension.
Basis and Dimension.
10. The Four Fundamental Subspaces.
Computing the Four Fundamental Subspaces.
11. Matrix Spaces; Rank 1; Small World Graphs.
Matrix Spaces.
12. Graphs, Networks, Incidence Matrices.
Graphs and Networks.
13. Quiz 1 Review.
Exam #1 Problem Solving.
14. Orthogonal Vectors and Subspaces.
Orthogonal Vectors and Subspaces.
15. Projections onto Subspaces.
Projection into Subspaces.
16. Projection Matrices and Least Squares.
Least Squares Approximation.
17. Orthogonal Matrices and Gram-Schmidt.
Gram-Schmidt Orthogonalization.
18. Properties of Determinants.
Properties of Determinants.
19. Determinant Formulas and Cofactors.
Determinants.
20. Cramer's Rule, Inverse Matrix, and Volume.
Determinants and Volume.
21. Eigenvalues and Eigenvectors.
Eigenvalues and Eigenvectors.
22. Diagonalization and Powers of A.
Powers of a Matrix.
23. Differential Equations and exp(At).
Differential Equations and exp (At).
24. Markov Matrices; Fourier Series.
Markov Matrices.
24b. Quiz 2 Review.
Exam #2 Problem Solving.
25. Symmetric Matrices and Positive Definiteness.
Symmetric Matrices and Positive Definiteness.
26. Complex Matrices; Fast Fourier Transform.
Complex Matrices.
27. Positive Definite Matrices and Minima.
Positive Definite Matrices and Minima.
28. Similar Matrices and Jordan Form.
Similar Matrices.
29. Singular Value Decomposition.
Computing the Singular Value Decomposition.
30. Linear Transformations and Their Matrices.
Linear Transformations.
31. Change of Basis; Image Compression.
Change of Basis.
33. Left and Right Inverses; Pseudoinverse.
Pseudoinverses.
32. Quiz 3 Review.
Exam #3 Problem Solving.
34. Final Course Review.
Final Exam Problem Solving.
Taught by
Prof. Gilbert Strang
Tags
Reviews
5.0 rating, based on 3 Class Central reviews
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Good teaching, and easy to learning linear algebra course teaches well and I learning well. Our problem solving method is very easy to understand.
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Nice experience and I learnt many things on the course which I took and nive explained 👌.
And Avery line to line they I have been explained nice thank for explain in understanding way -
This course has been incredibly beneficial. I've gained extensive knowledge in linear algebra, thanks to the clear and thorough explanations of the concepts.