MTH 451 LEARNING RESOURCES

Matlab is an interpretive programming language, built on a basic linear algebra construct and optimized linear algebra package. It is ideally suited for learning linear algebra, and was developed by a terrific linear algebra scientist, Cleve Moler. It is FREE TO OSU Students!
To start: This is an old but really simple 1st tutorial on matlab. Should take you 40 mins to go through these notes.
After the primer, try the set of instructions on this page . (this is a homework for a totally different class, ignore references to the other class).

A Gram Schmidt Illustration using matlab
A simple QR example using matlab
A least squares matlab example A code that shows how poorly conditioned polynomial interpolation can get.

An SVD Demo . (I found this on line. I have to find the person who wrote it so that I can give him/her credit). You will need the "Lena" image. There is an amusing story behind Lena Sodderberg's connection to image processing (search it).

Another SVD Demo . You will need the "Mona Lisa" image. To run this demo, open the SVDexample.mlx using the matlab open tab on the editor and then use the toggle (Run all). mlx files can be fragile, so if things are not working, type SVDexample on the command prompt in matlab. The executable portion of the code will run. Make sure that the code and the jpg image are in the same directory and that matlab choice of directory is the same.
A mathematica demo that shows how the fixed point iteration proceeds on a variety of functions.

Python is actually a meta-language with all sorts of capabilities, extremely useful (scripting, symbolics, numerics, etc); much more to learn but you can adopt python for a great many things. All of the above programs have strengths and weaknesses, but no one will fall short of delivering a great deal of productivity, for the price.

Mathematica is a popular computing package, with amazing capabilities. It's capabilities make it impossible to call it a symbolic program. It was developed by Stephen Wolfram, a theoretical physicist who has been fascinated by computing and with cellular automata. IT IS FREE TO OSU students! Mathematica is very easy to learn and will be extremely useful in classes, and in your future engineering, or scientific career, or professional career. Mathematica has a great many tutorials and help pages at its web site. If you've never used it, the very first thing to do is to view This beginner 2-part tutorial. After that you can go to the learning center and the knowledge base. For fun you should check out mathematica alpha. Note: mathematica CDF files do not require you to have mathematica. You do need to get the CDF player, which is available for free from WOLFRAM , the company the produces Mathematica. The nb files require using mathematica.
  • A 2D SVD Example that emphasizes basic transformations (See Lecture 4 of Trefethen and Bau).
  • An SVD Image Compression Example (See Lecture 5 of Trefethen and Bau).
  • A QR Example (See Lecture 7 of Trefethen and Bau).
  • A Gram Schmidt Example (See Lecture 8 Trefethen and Bau).
  • A Least Squares Demo (See Lecture 11 of Trefethen and Bau).