Gerschgorin's disk Thm (a test)

plot eigenvalue on complex plane show that all these points located in such circles.

Description

% ------------------------------------------------------
% 4-1
% test for Gerschgorin's disk Thm with A a C(m*m) matrix
% ex : >>testGerschgorin(A) ;
% % plot eigenvalues in redx located in these circles
% note : you could use this without input A as a demo
% ------------------------------------------------------
% Summit.Suen(at)NTUMath
% [e-mail]
% 14.May.2007
% 17.May.2007 revised

• MATLAB release: MATLAB 6.5 (R13)

[John D'Errico]

I hope the author realizes that a 3 rating from me for this submission is quite a complement for a student submission to the FEX. (I probably wanted to rate it a 2.75, but I rounded up.)

What do I like about this submission? It has some help. It has internal comments that explain what was done. It even supplies a default for its one argument. It is not a script file. All these aspects are good.

What does this lack? I'd suggest better help for it. A Gershgorin disk code is a teaching tool as its main value. It would rarely be of any value for anything else. And since it does nothing but produce a plot, this really is purely expositional. The point is that a teaching tool, aimed at other students or anyone who is just learning about the subject, should have VERY good help. It should explain what you are seeing.

How would I improve this tool? Were I to have done it myself, I'd have included a .mat file with some carefully constructed matrices that have intersting properties for Gershgorin disks. For example, come up with a matrix that has an eigenvalue that lies exactly on the perimeter of one of the disks. Provide a matrix that has disjoint disks, where some eigenvalues lie in each disk. Provide a non-singular matrix, where Gershgorin disks clearly prove that the matrix must be non-singular. Then I'd use publish to create a demo file that explains what properties each provided matrix has, and what Gershgorin disks tell us about the matrix.

What else would I do? I'd provide links to Wikipedia, or Mathworld, explaining in detail what Gershgorin diska are
and what they tell you about a matrix.

Finally, the author might have included an H1 line. The is the first line of help. It should be a one line description of the function, including some good key words. This is what the lookfor command keys on. Note that next year, when someone wants to find this function, how else will they know to look for "testGershgorin" from a list of hundreds of functions? Lookfor will find it nicely, IF you enable it.

I hope the author will continue to grow in Matlab skills. This submission shows promise for what we will see in the future from the author. However, I would suggest that the author look mainly to provide tools that provide actual utility to those who will browse through the file exchange.