Re: Symbolic question

[Jaroslav Hajek]

On Wed, Aug 5, 2009 at 12:44 PM, FrenchLeaf<address@hidden> wrote:
>
> Hello,
>
> I want to resolve the following problem :
>
> Det(alpha*F1 +(1 - alpha)*F2) == a3*lambda + a2*lambda + a1 *lambda +a0 = 0
>
> F1 and F2 are 3*3 matrix. Alpha is a single value.
> The problem is from the formula of the right of I can obtain the a3,a2,a1,a0
> factor to compute the lambda roots.
>

What you probably want to get (although your description is quite
incomprehensible) is called the generalized eigenvalues;
that means, roots of the polynomial p(alpha) = det (A - alpha*B) = 0.
Here, A = F2 and B = F2 - F1.

So, in Octave, you can either use
alpha = eig (F2, F2 - F1);
or
alpha = eig ((F2 - F1) \ F2); # faster, but only works if (F2 - F1) is
sufficiently regular.

of course Octave is a numerical tool, so you get only numerical answers.

-- 
RNDr. Jaroslav Hajek
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz