Re: Question
- Subject: [mg2911] Re: Question
- From: danl (Daniel Lichtblau)
- Date: 9 Jan 1996 04:31:49 -0600
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: Wolfram Research, Inc.
- Sender: mj at wri.com
In article <4cgrt5$im4 at dragonfly.wri.com> coppelli at sun3.dsea.unipi.it
(Alessandro Coppelli) writes:
>
> Hi to all.
>
>
> Question for guru in mathematica:
>
>
> 1) If I have the problem ..A x = lamba B x .. with B singular which
> program I must be used for to find lamba
>
We do not have a built-in generalized eigenvalues routine. Here is a
routine that will do the job, although the numeric stability might be
questionable.
genEigval[A_, B_, lam_] := Module[{n=Length[A], vals, gendet, rank},
rank = Length[SingularValues[B][[2]]];
vals = Map[Det[A-#*B]&, Table[j, {j, 1, rank+1}]];
gendet = InterpolatingPolynomial[vals, lam];
lam /. Solve[gendet==0, lam]
]
> 2) If I have the lamba matrix ( A(lamba) ) which program I must be
used
> for factoring A in A(lamba)=H(lamba) *
diag(P1(lamba).....Pn(lamba)) * K(lamba)
> with H and K not singular matrix and Real
I may not understand your question. Taking a guess, I'd say you probably
want SingularValues[...].
> 3) If I have the lamba matrix which program I must be used for applied
the
> method Gauss/Jordan on A(lamba)
Again, I'm guessing. You perhaps want to use RowReduce[...].
Daniel Lichtblau
WRI