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        riddles >> cs >> Find the eigenvectors on the TI-89
        
(Message started by: malchar on Apr 9^th, 2010, 7:59pm)

Title: Find the eigenvectors on the TI-89
Post by malchar on Apr 9^th, 2010, 7:59pm

This is probably real easy for most of the people in this forum. Anyway, I'm just finishing my first year of computer science, and I've taken to making my own programs on the TI-89 (graphing calculator). I'm still working on my current program, but maybe someone else would be interested since it's a pretty easy introduction to CS.

Create a program that takes a matrix and displays the eigenvalues and eigenvectors.

The problem I'm currently mulling over is how to properly calculate and output the case where certain eigenvalues are duplicates, in which the associated eigenvector should be a multidimensional span.

Title: Re: Find the eigenvectors on the TI-89
Post by Obob on Apr 9^th, 2010, 8:26pm

Last I checked, a TI-89 has built in eigenvector and eigenvalue commands...

If you want to code it from more elementary functions, you'll need to really come to grips with the linear algebra. In particular, if you have repeated eigenvalues, it doesn't automatically mean you have a multidimensional eigenspace: for instance, the matrix

1 1
0 1

has the eigenvalue 1 with multiplicity 2, but its only eigenvector is the vector (1,0).

Unless the calculations are being performed exactly, numerical stability is a huge issue in trying to find eigenvectors and eigenvalues by computer. The algorithm you would use to find eigenvectors and eigenvalues by hand is poorly suited to computer implementation, especially if you matrix might be defective (i.e. is non-diagonalizable).

Title: Re: Find the eigenvectors on the TI-89
Post by malchar on Apr 10^th, 2010, 12:37pm

Yes, they do already have those functions. Anyway, I didn't know quite how hard it would be to make my own programs. I'll continue to work with it a bit.