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From: wtanksle AT sdcc15 DOT ucsd DOT edu (William Tanksley)
Newsgroups: comp.os.msdos.djgpp
Subject: Re: 3*3 eigenvalues
Date: Mon, 18 Dec 1995 07:05:08 -0500
Organization: University of California, San Diego
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Message-ID: <4b2ao9$4ed@sdcc12.ucsd.edu>
References: <DJL4wn DOT 2zr AT jade DOT mv DOT net> <4at2kg$n2a AT micro DOT internexus DOT net>
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To: djgpp AT delorie DOT com
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master AT micro DOT internexus DOT net (Laszlo Vecsey) wrote to us all:
>A.Appleyard (A DOT APPLEYARD AT fs2 DOT mt DOT umist DOT ac DOT uk) wrote:
>: I have written a C function to work out eigenvalues and eigenvectors of 3*3
>: matrixes quickly and without iterating, if anybody out there is interested.

>Well, now that you got our attention, tell us what they are so we can 
>determine if we're interested! (Or am I the only one that doesn't know 
>what eigen values are and what they are useful for? I hope not)

You're not the only one.  However, I do happen to know, and I can tell you
this: if you don't already know, it's because the knowledge wouldn't help
you.

Here's a rough summary: a matrix can be used to transform a vector in
certain ways.  It turns out that for certain vectors, the transformation
they undergo because of that matrix is quite simple, just extending or
contracting them a constant amount, without rotation or any other odd
effects.  Well, it turns out that extension or contraction is the result of
multiplying the vector by some scalar (i.e. an ordinary number).  That
scalar is one of the eigenvalues of that matrix.  The vector that it
transforms so neatly is its eigenvector.

For a matrix with N columns and N rows, there are N eigenvalues.  Each
eigenvalue has one normal eigenvector associated with it.

This explanation is purposely difficult; to make it useful I would have to
spend a semester teaching it to you.  Thus, I give you only a general intro
to the theory.  For more and better information, see a teacher of 'Linear
Algebra'.

-Billy