TI-83 Plus: Is it possible to find the eigenvalues on this calculator?

Question

I searched the Internet and can't seem to find a source on how to find the eigenvalues on a TI-83 Plus calculator. Can anyone give me a hand?

Answer 1

The thing with the TI-83 Plus is that although there aren't any built-in functions for finding the eigenvalues of a matrix, you do have a usable programming language at your disposal for writing a program to do it for you.

To that end, I had translated (a very long time ago!) some of the algorithms from the venerable FORTRAN package EISPACK into TI-BASIC. In particular, for the case of finding the eigenvalues of some general real matrix, I translated the FORTRAN routines elmhes() (similarity transformation of a matrix to upper Hessenberg form via Gauss transforms) and hqr() (the Francis QR algorithm for upper Hessenberg matrices) into the TI-BASIC routines prgmHESGAU and prgmEIGVAL, respectively. You can download these two programs (zipped up) from here; if you want to see the code before committing them to your calculator, you can use SourceCoder.

Briefly, the way to use these is to input the matrix whose eigenvalues you want into the matrix [H], run prgmHESGAU first (optionally deleting matrix [I] if you're pressed for space) and then run prgmEIGVAL. The eigenvalues of your matrix will be in the list ∟EIG (so input something like [[1,4,2][2,-3,1][0,2,-5]]→[H]:prgmHESGAU:prgmEIGVAL:∟EIG).

I won't be discussing the algorithms behind them here; suffice it to say that these two are the practical applications of the fact that similarity transformations of a matrix preserve eigenvalues. Note that this set computes eigenvalues only; if eigenvectors are needed as well, then the programs are slightly more complicated, and I'll edit this answer to include those routines if there's interest.

Answer 2

Not really an answer, but if you have a TI-83 Plus, you can use the polynomial root application to find all the roots of the characteristic polynomial (if your calculator doesn't have this application, you can get it online from TI). If it's a normal TI-83, I think there's a numerical solver under the math menu, but that might not help a lot to find complex zeros. Perhaps ticalc.org has something?

Answer 3

The chart on page 11 here indicates that this might be a problem (for TI-83 PLUS).