MIT 18.06SC Linear Algebra, Fall 2011

MIT 18.06SC Linear Algebra, Fall 2011

An Interview with Gilbert Strang on Teaching Linear Algebra

MIT 18.06SC Linear Algebra, Fall 2011
Instructor: Gilbert Strang, Sarah Hansen
View the complete course: https://ocw.mit.edu/18-06SCF11
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63uMA4q8GaU6Eg5nzeOc8tx
In this video, Professor Gilbert Strang shares how he infuses linear algebra with a sense of humanity as a way to engage students in learning mathematics.
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Course Introduction | MIT 18.06SC Linear Algebra

MIT 18.06SC Linear Algebra, Fall 2011
Instructor: Gilbert Strang
View the complete course: https://ocw.mit.edu/18-06SCF11
YouTube Playlist: https://www.youtube.com/playlist?list=PL221E2BBF13BECF6C
Professor Gil Strang describes the key concepts of undergraduate course Linear Algebra, who should take it, and how it is taught. He provides examples of applications of linear algebra and how it is useful in physics, economics and social sciences, natural sciences, and engineering.
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1. The Geometry of Linear Equations

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
1. The Geometry of Linear Equations
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Geometry of Linear Algebra

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on the geometry of linear algebra.
Watch this in Chinese: https://youtu.be/mgbjhzDndOY
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Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Recitation 1: Key ideas of linear algebra
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An Overview of Key Ideas

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Martina Balagovic
A teaching assistant introduces key ideas found in the course 18.085.
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2. Elimination with Matrices.

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list…
2. Elimination with Matrices.
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Elimination with Matrices

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Martina Balagovic
A teaching assistant works through a problem on elimination with matrices.
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3. Multiplication and Inverse Matrices

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
3. Multiplication and Inverse Matrices
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Inverse Matrices

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ana Rita Pires
A teaching assistant works through a problem on inverse matrices.
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4. Factorization into A = LU

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
4. Factorization into A = LU
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LU Decomposition

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ben Harris
A teaching assistant works through a problem on LU decomposition.
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5. Transposes, Permutations, Spaces R^n

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
5. Transposes, Permutations, Spaces R^n
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Subspaces of Three Dimensional Space

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on subspaces of three dimensional space.
Watch this video in Chinese: https://youtu.be/VyPIQ_8QqEk
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6. Column Space and Nullspace

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
6. Column Space and Nullspace
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Vector Subspaces

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Nikola Kamburov
A teaching assistant works through a problem on vector subspaces.
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7. Solving Ax = 0: Pivot Variables, Special Solutions

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
7. Solving Ax = 0: Pivot Variables, Special Solutions
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Solving Ax=0

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Martina Balagovic
A teaching assistant works through a problem on solving Ax=0.
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8. Solving Ax = b: Row Reduced Form R

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
8. Solving Ax = b: Row Reduced Form R
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Solving Ax=b

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
YouTube Playlist: https://www.youtube.com/playlist?list=PL221E2BBF13BECF6C
Instructor: Martina Balagovic
A teaching assistant works through a problem on solving Ax=b.
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9. Independence, Basis, and Dimension

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
9. Independence, Basis, and Dimension
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Basis and Dimension

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ana Rita Pires
A teaching assistant works through a problem on basis and dimension.
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10. The Four Fundamental Subspaces

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
10. The Four Fundamental Subspaces
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Computing the Four Fundamental Subspaces

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ben Harris
A teaching assistant works through a problem on the four fundamental subspaces.
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11. Matrix Spaces; Rank 1; Small World Graphs

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
11. Matrix Spaces; Rank 1; Small World Graphs
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Matrix Spaces

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ana Rita Pires
A teaching assistant works through a problem on matrix spaces.
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12. Graphs, Networks, Incidence Matrices

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
12. Graphs, Networks, Incidence Matrices
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Graphs and Networks

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Nikola Kamburov
A teaching assistant works through a problem on graphs and networks.
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13. Quiz 1 Review

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
13. Quiz 1 Review
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Exam #1 Problem Solving

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Nikola Kamburov
A teaching assistant introduces problems found in the first exam.
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14. Orthogonal Vectors and Subspaces

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
14. Orthogonal Vectors and Subspaces
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Orthogonal Vectors and Subspaces

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: David Shirokoff
A teaching assistant works through a problem on orthogonal vectors and subspaces.
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15. Projections onto Subspaces

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
15. Projections onto Subspaces
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Projection into Subspaces

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Nikola Kamburov
A teaching assistant works through a problem on projection into subspaces.
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16. Projection Matrices and Least Squares

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
16. Projection Matrices and Least Squares
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Least Squares Approximation

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ben Harris
A teaching assistant works through a problem on least squares approximation.
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17. Orthogonal Matrices and Gram-Schmidt

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
17. Orthogonal Matrices and Gram-Schmidt
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Gram-Schmidt Orthogonalization

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ana Rita Pires
A teaching assistant works through a problem on Gram-Schmidt orthogonalization.
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18. Properties of Determinants

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
18. Properties of Determinants
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Properties of Determinants

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ana Rita Pires
A teaching assistant works through a problem on properties of determinants.
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19. Determinant Formulas and Cofactors

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
19. Determinant Formulas and Cofactors
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Determinants

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on determinants.
Watch this video in Chinese: https://youtu.be/ZyYGJc9jNno
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20. Cramer's Rule, Inverse Matrix, and Volume

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
20. Cramer’s Rule, Inverse Matrix, and Volume
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Determinants and Volume

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on determinants and volume.
Watch this video in Chinese: https://youtu.be/ZuWAwCEMeWE
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21. Eigenvalues and Eigenvectors

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
21. Eigenvalues and Eigenvectors
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Eigenvalues and Eigenvectors

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Nikola Kamburov
A teaching assistant works through a problem on eigenvalues and eigenvectors.
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22. Diagonalization and Powers of A

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
22. Diagonalization and Powers of A
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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.
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23. Differential Equations and exp(At)

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
23. Differential Equations and exp(At)
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Differential Equations and exp (At)

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on differential equations.
Watch this video in Chinese: https://www.youtube.com/watch?v=fiSp3Ss-Yo8
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24. Markov Matrices; Fourier Series

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
24. Markov Matrices; Fourier Series
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Markov Matrices

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: David Shirokoff
A teaching assistant works through a problem on Markov matrices.
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24b. Quiz 2 Review

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
24b. Quiz 2 Review
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Exam #2 Problem Solving

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through problems found on the second exam.
Watch this video in Chinese: https://youtu.be/ThxvK9t7DNo
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25. Symmetric Matrices and Positive Definiteness

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
25. Symmetric Matrices and Positive Definiteness
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Symmetric Matrices and Positive Definiteness

MIT 18.06SC Linear Algebra, Fall 2011
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Instructor: David Shirokoff
A teaching assistant works through a problem on symmetric matrices and positive definiteness.
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26. Complex Matrices; Fast Fourier Transform

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
26. Complex Matrices; Fast Fourier Transform
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Complex Matrices

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: David Shirokoff
A teaching assistant works through a problem on complex matrices.
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27. Positive Definite Matrices and Minima

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
27. Positive Definite Matrices and Minima
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Positive Definite Matrices and Minima

MIT 18.06SC Linear Algebra, Fall 2011
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Instructor: Martina Balagovic
A teaching assistant works through a problem on positive definite matrices and minima.
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28. Similar Matrices and Jordan Form

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
28. Similar Matrices and Jordan Form
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Similar Matrices

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ben Harris
A teaching assistant works through a problem on similar matrices.
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29. Singular Value Decomposition

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
29. Singular Value Decomposition
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Computing the Singular Value Decomposition

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ben Harris
A teaching assistant works through a problem on computing the singular value decomposition.
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30. Linear Transformations and Their Matrices

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
30. Linear Transformations and Their Matrices
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Linear Transformations

MIT 18.06SC Linear Algebra, Fall 2011
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Instructor: Nikola Kamburov
A teaching assistant works through a problem on linear transformations.
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31. Change of Basis; Image Compression

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
31. Change of Basis; Image Compression
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Change of Basis

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Martina Balagovic
A teaching assistant works through a problem on change of basis.
License: Creative Commons BY-NC-SA
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33. Left and Right Inverses; Pseudoinverse

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
33. Left and Right Inverses; Pseudoinverse
License: Creative Commons BY-NC-SA
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Pseudoinverses

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: David Shirokoff
A teaching assistant works through a problem on pseudoinverses.
License: Creative Commons BY-NC-SA
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32. Quiz 3 Review

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
32. Quiz 3 Review
License: Creative Commons BY-NC-SA
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Exam #3 Problem Solving

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: David Shirokoff
A teaching assistant introduces problems found on the third exam.
License: Creative Commons BY-NC-SA
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34. Final Course Review

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
34. Final Course Review
License: Creative Commons BY-NC-SA
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Final Exam Problem Solving

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Ana Rita Pires
A teaching assistant works through a problem on the final exam.
License: Creative Commons BY-NC-SA
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More courses at https://ocw.mit.edu