Re: QUESTION (EigenVectors)

• To: mathgroup at smc.vnet.net
• Subject: [mg19417] Re: QUESTION (EigenVectors)
• Date: Mon, 23 Aug 1999 13:57:24 -0400
• Organization: Deja.com - Share what you know. Learn what you don't.
• References: <7pl79i\$ch0@smc.vnet.net>
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```Mathematica has built-in routines for finding the eigenvalues and
eigenvector of any n-by-n matrix.  See the help under List and
Matrices -> Matrix Operations -> EigenValues, EigenVectors and
EigenSystem.

EigenValues[matrix] gives you the roots of the n-degree polynomial.
EigenVectors[matrix] gives the EigenVector.
EigenSystem[matrix] gives both the eigenvalues and corresponding
eigenvector in one command.

In article <7pl79i\$ch0 at smc.vnet.net>,
clangis at chat.carleton.ca (Christian Langis) wrote:
> Hi there.
>
> I am a a computer science student; and that is probably why
> this question may seem deprived of any chalenge to you. But it
> is quite challenging to me.
>
> The question is: how do you extract the 1st EigenVector from a
> 3x3 matrix (and optionally 2nd and 3rd)?
>
> I read a solution which forces the person to extract the 3
> roots of a 3rd degree polynomial. And this has to be done by
> hand of course.
>
> Hence, it is possible to compute that manually. But I am rather
> looking for an algorithm do carry this task, a solution which
> does not involve any manual evaluation (such as root extraction).
>
> Therefore do you know any algorithm/source code to do that (or
> know where to find it)?
>
> thanks
>
>

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```

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