"You see this little hole? This moth's just about to emerge. It's in there right now, struggling. It's digging it's way through the thick hide of the cocoon. Now, I could help it - take my knife, gently widen the opening, and the moth would be free - but it would be too weak to survive. Struggle is nature's way of strengthening it."

--Locke (

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• The author, Gilbert Strang of MIT taught Linear Algebra in the Fall of 2011 out of his textbook. The lectures were videotaped and are part of the MIT OpenCourseWare (OCW) project. These lectures are

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1. Geometry of linear equations. Strang: Lecture 1, Sections 1.1, 1.2, 2.1.

2. Key ideas of linear algebra .

3. Elimination with matrices . Strang: Lecture 2, Sections 2.2, 2.3.

4. Multiplication and inverse matrices. Strang: Lecture 3, Sections 2.4, 2.5.

5. LU-factorization. Strang: Lectures 4 & 5 (1st half), Sections 2.6, 2.7.

6. Vector spaces, column space, and row space. Strang: Lectures 5 (2nd half) & 6, Sections 3.1, 3.2.

7. Solving Ax=0: Pivot and free variables. Strang: Lecture 7, Section 3.2.

8. Solving Ax=b: Homogeneous and particular solutions. Strang: Lecture 8, Sections 3.3, 3.4.

9. Linear independence, spanning sets, and bases. Strang: Lecture 9, Section 3.5.

10. The four fundamental subspaces. Strang: Lecture 10, Section 3.6.

11. Other vector spaces. Strang: Lecture 11, Section 3.2.

12. Application: Graphs and networks. Strang: Lecture 12, Section 8.2.

1. Orthogonality. Strang: Lecture 14, Section 4.1.

2. Projections. Strang: Lecture 15, Section 4.2.

3. Least squares. Strang: Lecture 16, Section 4.3.

4. Orthogonal bases and Gram-Schmidt. Strang: Lecture 17, Section 4.4.

5. Determinants. Strang: Lecture 18, Section 5.1.

6. Formulas for determinants. Strang: Lecture 19, Section 5.2.

7. Applications of determinants. Strang: Lecture 20, Section 5.3.

8. Eigenvalues and eigenvectors. Strang: Lecture 21, Section 6.1.

9. Diagonalization. Strang: Lecture 22, Section 6.2.

10. Application: Markov chains. Strang: Lecture 24 (1st part), Section 8.3.

11. Application: Fourier series. Strang: Lecture 24 (2nd part), Section 8.5.

1. Symmetric matrices. Strang: Lecture 25 (1st part), Section 6.4.

2. Positive definite matrices Strang: Lectures 25 (2nd part) & 27, Section 6.5.

3. Complex matrices. Strang: Lecture 26, Section 10.1, 10.2, 10.3.

4. Similar matrices and Jordan canonical form. Strang: Lecture 28, Section 6.6.

5. Singular value decomposition. Strang: Lecture 29, Section 6.7.

6. Linear transformations. Strang: Lecture 30, Section 7.1, 7.2.

7. Change of basis. Strang: Lecture 31, Section 7.2, 7.3.

8. Left, right, and pseudoinverses. Strang: Lecture 32, Section 7.2, 7.3.