Re: How does Eigensystem works ?
- To: mathgroup at smc.vnet.net
- Subject: [mg103111] Re: How does Eigensystem works ?
- From: pfalloon <pfalloon at gmail.com>
- Date: Tue, 8 Sep 2009 05:58:49 -0400 (EDT)
- References: <h829hp$3pk$1@smc.vnet.net>
On Sep 7, 4:34 pm, guerom00 <guero... at gmail.com> 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] ! > > What gives? > > Thanks If you check out the definitions it makes perfect sense: P = matrix with eigenvectors as columns. Eigenvectors[matrix] (or Eigensystem[matrix][[2]]) = list of eigenvectors, which is equivalent to a matrix with eigenvectors as rows. So, you need to Transpose the latter to get P.