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Re: How does Eigensystem works ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg103103] Re: How does Eigensystem works ?
  • From: Alois Steindl <alois.steindl at jet2web.cc>
  • Date: Tue, 8 Sep 2009 05:57:21 -0400 (EDT)
  • References: <h829hp$3pk$1@smc.vnet.net>

guerom00 schrieb:
> Hello everyone,
> 
> If I compute the eigenvalues lambda and eigenvectors P of a square
> matrix A, I get the original matrix back by calculating Transpose
> [P].DiagonalMatrix[lambda].Transpose[Inverse[P]] ???
> 
> Now, I don't know much in linear algebra but I think I should get the
> origonal matrix back by computing P.DiagonalMatrix[lambda].Inverse
> [P] !
> 
> What gives?
> 
> Thanks
> 
Hello,
that's, because
{eval, evec}=Eigensystem
returns the transpose of the matrix P in evec: The i-th element of evec 
contains the i-th eigenvector, whereas in

A = P.diag(lambda).Inverse[P]
one expects the i-th eigenvector in column i.

Alois


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