MIT 18.06SC Linear Algebra, Fall 2011

Instructor: Gilbert Strang The Help Session Videos were developed by: Martina Balagovic, Linan Chen, Benjamin Harris, Ana Rita Pires, David Shirokoff, Nikola Kamburov View the complete course: http://ocw.mit.edu/18-06SCF11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Curated by: MIT OpenCourseWare (74 videos)

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Currently Playing: Powers of a Matrix

MIT 18.06SC Linear Algebra, Fall 2011 View the complete course: https://ocw.mit.edu/18-06SCF11 Instructor: Ben Harris A teaching assistant worksthrough a problem on powers of a matrix. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

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Tracks in this Playlist

• 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