       Re: Question

• To: mathgroup at smc.vnet.net
• Subject: [mg2911] Re: Question
• From: danl (Daniel Lichtblau)
• Date: Tue, 9 Jan 1996 02:18:44 -0500
• Organization: Wolfram Research, Inc.

```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][]];
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

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```

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