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