There is an unusually large number of commands on the TI-68k calculators dealing with matrices (as you may have noticed from reading the article). I've tried to present them in in groups, dividing them into categories based roughly on the way they work. As a result, however, the list on the bottom of the page isn't complete (although I think if I tried to cover every matrix command, I'd end up listing half the catalog).
Date: 13 Feb 2008 04:40
Number of posts: 6
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Now that I'm thinking about it… DarkerLine, should you come to writing the pages for the 68k eigenroutines, could you try to include a demonstration of what happens when you feed it a Jordan block?
What exactly did you have in mind?
Well, could you show what the output of eigVc looks like for a Jordan block (you can use [[1,1,0][0,1,0][0,0,1]] as an example)? The QR algorithm (the algorithm internally used for computing eigenvalues/vectors) will either be setup to return a single vector, padded with zeros to make a square matrix, or return three (nearly) parallel/collinear vectors, and I'm curious as to what behavior TI chose.
Also probably do it side by side with, say, eigVc(identity(3)), showing that a multiple eigenvalue doesn't imply defectiveness.
eigVc() returns [[1,-1,0][0,1.e-15,0][0,0,1]] (which is fairly typical of other results) — that is, instead of zero vectors, there's nearly-zero vectors. The calculator still detects this matrix as singular even though it's technically not (and the determinant is calculated as 0 instead of 1.e-15)
I don't know when I'll get to those commands, though, although it might make sense to just get them over with now.
From the page:
"Since occasionally you want to do these operations element-by-element, the alternatives .+, .-, .*, ./, and .^ have been provided, which do this for both two matrices and for a matrix and an expression."
This is actually borrowed MATLAB notation. Moler and others also recognized that there are applications for operating element-wise instead of taking the matrix as a whole, and thus put in support for the math operators preceded with a dot.