Re: How does Eigensystem works ?
- To: mathgroup at smc.vnet.net
- Subject: [mg103121] Re: How does Eigensystem works ?
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Tue, 8 Sep 2009 06:00:38 -0400 (EDT)
- References: <h829hp$3pk$1@smc.vnet.net>
On 2009.09.07. 8:34, guerom00 wrote: > 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] ! > This would be true if the eigenvectors were columns in P. But in Mathematica they're rows. Eigenvalues[mat] is not a matrix with the eigenvectors as columns, but simply a *list of eigenvectors*, which in Mathematica happens to be the same things as a matrix with the eigenvectors as rows.