April 16, 2015
This exercise is due Tuesday, April 21, at the beginning of lecture.
Find the Singular Value Decomposition of
(I am not so interested in the specific answer, which can be found online, but rather in the process describing how one arrives to this answer.)
April 8, 2015
This problem is due April 30 at the beginning of lecture.
Write a program that receives as input a real symmetric matrix and some tolerance bound , and performs the basic method to generating (and printing) a sequence of matrices until a stage is reached where the entries below the diagonal of are all in absolute value below . Once this happens, the program returns the diagonal entries of as approximations to the eigenvalues of . (Check on a couple of examples that these are indeed decent approximations, at least for of small size and reasonably small values of .)
Most Computer Algebra Systems already have implemented algorithms to find the decomposition of a matrix. Instead of using these pre-programmed algorithms, write your own.
(Turn in the code, plus the couple of examples. Comment your code, so it can be easily understood what you are doing along the way. I’m reasonably familiar with Maple, Mathlab, Sage, and most flavors of C. If you are going to use a different language, please let me know as soon as you can, to see whether it is something I’ll be able to verify or if a different language will be needed instead. Ideally, the user can choose the dimension of the input matrix.)
March 1, 2015
Our daughter decided to rush things up a bit, and is being born right now. You
probably will have someone else covering class for a couple of weeks, sorry for the inherent inconvenience. I’ll be updating as I know more.
[Edit (11:00am): Isabel. Office hours are cancelled March 3 and 10.]
February 5, 2015
This set is optional, and due February 12 at the beginning of lecture.
From Chapter 3 of Axler’s book, solve exercises 1,2,3,9,10,16, and 25.
(The numbering is as in the second edition. If you own the third edition, let me know and I’ll check in case the statements have changed.)