Path: utzoo!attcan!uunet!van-bc!ubc-cs!fs1!ee.ubc.ca!jmorriso
From: jmorriso@ee.ubc.ca (John Paul Morrison)
Newsgroups: comp.sys.handhelds
Subject: Re: matrix manipulations
Message-ID: <1990Nov12.122755@ee.ubc.ca>
Date: 12 Nov 90 20:27:54 GMT
References: <6132@quanta.eng.ohio-state.edu>
Sender: root@fs1.ee.ubc.ca
Reply-To: daveg@ee.ubc.ca
Organization: UBC Electical Engineering VLSI Lab
Lines: 68

The Eigenvector, eigenvalue problem is fairly easy.

write this program:
	<< A I L * - DET >>
Put your matrix in A, the identity matrix in I and then hit solve.
It helps to try and get a reasonable guess first.

This isn't exactly an EFFICIENT method, but it is EASY to do!

Eigenvectors are more tricky:
you have to calculate A-LI where L is the eigenvalue in question.
you can't just put a zero vector  on the stack and divide to get the answer.
You will just get the trivial zero solution.

Instead: find INV(A-L*I).
You will get a weird looking matrix, since a division by zero was done
somewhere.
But you can scale the matrix down, and you will have n linearly
dependent solutions.

The column vectors of the matrix are the eigenvectors. With a bit of
common sense,
(ie fiddling) you should be able  to see how many INdependent
eigenvectors there are.

To get the column vectors try this short program I wrote:
it is A\->V

%%HP: T(3)A(D)F(.);
\<< TRN ARRY\-> LIST\->
DROP DUP 1 - NEG \->
n m m1
  \<< m n 1 - * 1 + n
    FOR i m \->ARRY i
ROLLD m1
    STEP n
  \>>
\>>


and the reverse  process V\->A
takes n vectors and puts them in a matrix

%%HP: T(3)A(D)F(.);
\<< OVER SIZE 1 GET
DUP 1 - \-> n m m1
  \<< n m n 1 - * 1 +
    FOR i i ROLL
ARRY\-> DROP m1
    STEP { n m }
\->ARRY TRN
  \>>
\>>


***both these programs have trivial bugs which I have no intention of
fixing right  now.
A\->V won't work for a 1 * n matrix. V\->A won't work for 1 dimensional
vecotrs. If you don't
like it, don't do it.

Putting it all together:
calculate A I L * - INV A\->V

which gives n vectors. Divide any vector by it absolute value or its row
norm (RNRM) and 
then you have an eigenvector that is normalized or scaled to a useful
value.