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From: Inf <infinitysquared@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Eigenvalues Problem?
Date: Sun, 30 Dec 2007 01:55:00 -0800 (PST)
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On 30 Dec, 08:31, "Michael Nikki" <ni...@yahoo.com> wrote:
> Hello... Good Day.
> I Have A Problem With Eigenvalues polinomial characteristic.
>
> I've read some books to get eigenvalues.
>
> If A=2x2:
> a b
> c d
>
> then
>
> polinomial is: lambda^2 - (a+b)lambda + det(A)
>
> So
>
> If A=3x3
>
> a b c
> d e f
> g h i
>
> polinomial is: -lambda^3 + (a+b+c) lambda^2 -
> (db+gc+hf-ae-ei) lambda + det(A)
>
> so polinomial of eigenvalues is:
> (-1)^n lambda^n + (-1)^(n-1) S1 lambda^(n-1) + (-1)^(n-2) Sk
> lambda^(k) + Sn
>
> Where:
> n=matrix dimension
> s1=trace(A)
> Sn=det(A)
>
> I wanna ask how to get Sk?
>
> If I have 4 dimension:
>
> a b c d
> e f g h
> i j k l
> m n o p
>
> Thanks.

Michel,

Two points:

1) you are getting your traces wrong - they
should be the sum of the diagonal elements

so  If A=2x2:
> a b
> c d

then trace A =a+d not a+b, as you write.

2) generally, the characteristic polynomial is
obtained from det(A-lambda*I)
where I is the identity matrix, e.g. in the 2x2 case
I is

1 0
0 1

So you need to read up how to work out
determinants.

Hope this helps.

Inf.