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Re: Question

  • To: mathgroup at
  • 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> coppelli at  
(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  

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  
>      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  
>      method Gauss/Jordan on A(lamba)

  Again, I'm guessing. You perhaps want to use RowReduce[...].

  Daniel Lichtblau


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