Course 18.06: Linear Algebra (Spring 2006)

Department of Mathematics
Massachusetts Institute of Technology

General Information

Lecturer: Alan Edelman, room 2-343, e-mail edelman AT math

Lectures: MWF 11 room 54-100

Course Administrator: Alice Chan, room 2-588, phone 3-4110, e-mail alicec

Textbook: Introduction to Linear Algebra, 3rd Edition by Gilbert Strang published by Wellesley-Cambridge Press.

The press website includes a review of the book by Professor Herman Gollwitzer of Drexel University.

Recitations:

If you would like to change your recitation, please do so in the Undergraduate Math Office (2-108).

IMPORTANT:

Make sure you turn in homework to your assigned section. Also, if you are not yet assigned to any section, please choose one as soon as possible. NOTE: Recitation 10 (T2 in 2-131) has been cancelled. If you have not been reassigned yet, you MUST GO TO 2-108 to register for a different section.

#	Time	Room	Instructor	Office	Phone	E-mail@math.mit.edu
1	M 2	2-131	A. Kasimov	2-339	3-1715	kasimov
2	M 3	2-131	A. Kasimov	2-339	3-1715	kasimov
3	M 3	2-132	R. Lehman	2-251	3-7566	rclehman
4	T 10	2-132	F. Liu	2-333	3-7826	fuliu
5	T 11	2-132	P. Shor	2-369	3-4362	shor
6	T 12	2-132	P. Shor	2-369	3-4362	shor
7	T 1	2-131	F. Liu	2-333	3-7826	fuliu
8	T 1	2-132	A. Osorno	2-229	3-1589	aosorno
9	T 2	2-132	A. Osorno	2-229	3-1589	aosorno

Course information: (ps, pdf).
There has been some confusion about grades. The official breakdown (posted February 15, 2006) is Problem sets 15%, three exams 45%, final exam 40%. Please ignore any handouts or other information with other breakdowns.

Syllabus: (ps, pdf).

Basic MATLAB info:

Parallel MATLAB info:

http://www.interactivesupercomputing.com/

Goals of the Linear Algebra Course (html)

A Factorization Review (ps, pdf)

Glossary for Linear Algebra (ps, pdf)

Linear Algebra in a Nutshell (ps, pdf)

Linear Algebra and Music (pdf) This fascinating article, with MATLAB codes for music and for telephone tones and for recovering answering machine information, was contributed by Derrick Smith of Laney College in Oakland. Thank you!!

Problem Sets

Answers and Solutions to Selected Problems

Videos

Videos of Professor Strang's Fall 1999 Lectures

To improve your video experience, we have made it possible for visitors to download the streaming video files. Here's the URL structure for a link to an MIT OCW video lecture delivered in a streaming format:

  http://mfile.akamai.com/7870/rm/mitstorage.download.akamai.com/7870/18/18.06/videolectures/strang-1806-lec01-26aug1999-220k.rm

If you want to download the same file and play it off-line, use the following URL - the only difference is in the first part of the URL:

  http://ocw.mit.edu/ans7870/18/18.06/videolectures/strang-1806-lec01-26aug1999-220k.rm

This same basic approach will work for most (not all) of the MIT OCW streaming videos. Simply find the URL to the streaming media, and replace the first part of the URL:

  http://mfile.akamai.com/7870/rm/mitstorage.download.akamai.com/7870     with     http://ocw.mit.edu/ans7870

Demos

READ THIS ! There are new eigenvalue applets WITH SOUND (use Flashplayer)

eigen_sound This 3-minute demo shows eigenvectors of 2 by 2 matrices
power_method Powers AⁿV lead toward the top eigenvalue/eigenvector

eigen_sound is also broken into 7 independent pieces

Applet 1 Applet 2 Applet 3 Applet 4 Applet 5 Applet 6 Applet 7

MINI-LECTURES ON EIGENVALUES (with voice explanation)

Full Lecture (all eight together)

Or to view individually (about 2 minutes each)

JAVA DEMOS (these are interactive, without voice explanation)

Other Information

The 3rd edition (2003) of the textbook is now available!!

Instructors could write directly to gs@math.mit.edu to see the new book.
It has Worked Examples and many new features: Glossary, Conceptual
Questions and "Linear Algebra in a Nutshell" will be useful to everyone.

Glossary: (ps, pdf)

Conceptual Questions for Review: (ps, pdf)

Linear Algebra in a Nutshell: (ps, pdf)

A Basis for 3 by 3 Symmetric Matrices (ps, pdf)

Gram-Schmidt in 9 Lines of MATLAB (ps, pdf)

Gram-Schmidt orthogonalization -- a nice example (ps, pdf)

Additional MATLAB info:

Added on 11/19/2003: Here are the pictures resulting from the best rank 1, rank 5, rank 10, rank 20 and rank 50 approximations to a 499 by 750 black-and-white intensity matrix. The approximations were obtained by keeping the k largest singular values in the SVD. The bottom right picture is the original one.
Added on 11/3/2003: MATLAB diary from review lecture on 11/3/2003
MATLAB Teaching Codes
Best Guide to MATLAB
Cool MATLAB demos by The Mathworks.
MATLAB Recitation Demos from 1997

Question from Professor Ian Christie, West Virginia University:

Find unit vectors h(t) and m(t) in the direction of the hour and minute hands of a clock, where t denotes the elapsed time in hours. If t = 0 represents noon then m(0) = h(0) = (0,1). At what time will the hands of the clock first be perpendicular? At what time after noon will the hands first form a straight line? In the dot product m(t) * h(t), remember that sin x sin y + cos x cos y = cos(x - y). Solution: (ps, pdf)

Multiplication by Columns! The multiplication Ax produces a combination
of the columns of A. If the vectors a₁, a₂, ... , a_n are those columns, then

Ax = x₁ a₁ + ... + x_n a_n = combination of columns (in the column space!)

A summary of how the properties of different matrices are reflected in the eigenvalues/eigenvectors: (ps, pdf).

Pascal Matrices (new article by Alan Edelman and Gilbert Strang): (ps , pdf )

An Essay by Professor Strang: Too Much Calculus: (ps , pdf )

INTERESTING DEMOS:

Exams from Previous Years

More Practice Exams...

Welcome to MIT's Linear Algebra Home Page for Course 18.06!

You are visitor number since October 1, 1996.

Textbook:	Introduction to Linear Algebra, 3rd Edition by Gilbert Strang published by Wellesley-Cambridge Press.
	The press website includes a review of the book by Professor Herman Gollwitzer of Drexel University.