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