Linear Algebra MAT 26500 Sections 11,12
Click here for a course calendar.
It contains an outline of all the classes, the exam and review dates, holidays, exams, etc...
Important Dates:
First exam: October 1, 2009. Here are some practice problems, and here are some solutions (as usual,
may contain typos/mistakes/etc.. use with extreme caution, yada yada yada).
Second exam: Thursday November 12, 2009 Here is the exam along with some solutions Note: in the comments at the end there are
some square roots of pi that disappear for a short while starting in the middle of page 8, though they reappear in time to give the correct answer. I'm not
going to fix that at this point (I'd like to but I'm fed up with typing!), but if you read that part
you may want to be aware of that. Also I totally neglected the Fourier coefficient of the constant, but if you can understand what's going on it should be easy
to show that it's zero and therefore doesn't contriute to the discussion that follows.
Some practice problems for the second midterm. and some Partial solutions Caution! This document was made in a rush and there are
some errors that haven't been (and won't be) corrected.
Last lecture: December 10, 2009
Final exam: Wednesday December 16 @ 3:20pm (2 hours) It is in STEW 130 (which is, apparently, the auditorium "Fowler Auditorium/hall" in the Stewart building)
Since the final exam covers everything from day $1$, I'm not going to write a separate practice set for the exam - use the stuff above for the previous exams
to help. The only stuff that is on the final that hasn't been covered on previous exams is/are: linear transformations, eigenvals/vectors, diagonalization,
complex numbers/matrices (Appendix B), and linear constant coefficient ODEs. Use the homework as a guide for what to practice. Also, you will find it quite
useful to look at past exams for this course (some of which have multiple choice problems, quite similar to the exam we will write), which can be found following links from here ,
Assignments:
Assignment 1, due September 8 (this one is a little longer than usual: please don't leave it to the
last minute!)
Assignment 2, due September 15
Assignment 3, due September 22
Assignment 4, due September 29
Assignment 5, due October 20
Assignment 6, due October 27
Assignment 7, due November 3
Assignment 8, due November 24
Assignment 9, due December 1
Assignment 10, due December 8
Grading Policy.
Topics covered
Chapter 1: Linear Systems and Matrices
Chapter 2: Solving linear systems
Chapter 3: Determinants
Chapter 4: Real Vector Spaces
Chapter 5: Inner Product Spaces
Chapter 7: Eigen(values/vectors/spaces) and Diagonalization (and Spectral theorem)
Chapter 8: Applications of Eigen(values/vectors/spaces): 8.4 Linear ODE (But I'd also like to talk about Principle Component Analysis in 8.3 a little)
Some files, meant for some in class MATLAB demos hopefully...
The first three files are taken from/based on stuff from
http://amath.colorado.edu/courses/4720/2000Spr/Labs/Worksheets/Matlab_tutorial/matlabimpr.html
cell1.jpg Picture of a cell.
I.mat Some data. (A bitmap of the above cell)
imagereduce.m An uber-simple image
compression tactic: takes an SVD of the image and throws away components
corresponding to small singular values (user defines "small").
In practice, I think other methods more closely related to the Fourier transform
are used for image compression much more commonly, but I'm certainly no expert on the subject so don't take my word on
it! This just demonstrates one way one could do it, using the SVD. The SVD has
many other applications: see for example
http://expertvoices.nsdl.org/cornell-cs322/2008/04/07/netflix-prize/ (although in the end it appears other methods were used,
initially people were able to beat the original algorithm pretty well using "brain-dead-simple SVD methods" (quoted from the above)).
This stuff taken from
http://www.cns.atr.jp/~kmtn/imageMatlab/index.html:
blah Gaussian blurs a pixel-y image to
a smooth (but blurry) picture.
Lincoln Pixel-y picture of Lincoln.