MthSc 311, Fall 2012
MthSc 311, Fall 2012
"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 (Lost, 2004)
Resources
• Class
Syllabus
• Text: Introduction to Linear Algebra, 4th edition, by
Gilbert Strang.
• 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 not a
substitute for attending class, but are a great supplement.
Homework
Homework 1: pdf |
tex. Due
Wednesday, August 29th at 4pm.
Homework 2: pdf |
tex. Due
Wednesday, September 5th at 4pm.
Homework 3: pdf |
tex. Due
Wednesday, September 12th at 4pm.
Homework 4: pdf |
tex. Due
Wednesday, September 19th at 4pm.
Homework 5: pdf |
tex. Due
Wednesday, September 26th at 4pm.
Homework 6: pdf |
tex. Due
Wednesday, October 3rd at 4pm.
Homework 7: pdf |
tex. Due
Wednesday, October 10th at 4pm.
Homework 8: pdf |
tex. Due
Friday, October 19th at 4pm.
Homework 9: pdf |
tex. Due
Friday, October 26th at 4pm.
Homework 10: pdf |
tex. Due
Friday, November 2nd at 4pm.
Homework 11: pdf |
tex. Due
Monday, November 12nd at 4pm.
Homework 12: pdf |
tex. Due
Tuesday, November 20th at 4pm.
Homework 13: pdf |
tex. Due
Friday, November 30th at 4pm.
Homework 14: pdf |
tex. Due
Friday, December 7th at 4pm.
Lecture notes
Part I: Solutions of linear equations and vector spaces
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.
Part II: Orthogonality, determinants, and eigenvectors
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.
Part III: Positive definite matrices and applications
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.