orthonormal version of Eigensystem[]?
- To: mathgroup@smc.vnet.net
- Subject: [mg11620] orthonormal version of Eigensystem[]?
- From: sidles@u.washington.edu (John Sidles)
- Date: Thu, 19 Mar 1998 19:48:26 -0500
- Organization: University of Washington, Seattle
Dear Mathematica users I admire the version of Eigensystem[] on Mathematica very much. It is fast and accurate, even for the 1000 x 1000 symmetric real matrices than I am looking at. But Eigensystem[] has one very important limitation when solving a symmetric real matrix, or more generally when solving a complex Hermitian matrix. This limitation is poorly documented and can "bite" the unwary user, as I found from personal experience. Namely, although Eigensystem[] usually returns a set of orthonormal eigenvectors when given a real symmetric matrix, it is not *guaranteed* do so. Specifically in the case where two eigenvalues are degenerate, the returned eigenvectors are (occasionally but not always) grossly nonorthogonal. Now, this behavior is perfectly consistent with the documentation of Eigensystem[], which is completely silent on the issue of eigenvector orthonormality. The reason the behavior is aFrom mathgroup-adm@smc.vnet.net Sun Mar 22 03:23:15 1998 Received: by mrc.math.hr; id AA16040; Sun, 22 Mar 1998 03:23:13 +0100 Received: by smc.vnet.net. (SMI-8.6/SMI-SVR4) id SAA15258; Sat, 21 Mar 1998 18:35:00 -0500 Received: by smc.vnet.net. (SMI-8.6/SMI-SVR4) id SAA15254; Sat, 21 Mar 1998 18:34:59 -0500 Date: Sat, 21 Mar 1998 18:34:59 -0500 Message-Id: <199803212334.SAA15254@smc.vnet.net.> From: dimiter@shemesh.chem.purdue.edu (Dimiter Petsev) To: mathgroup@smc.vnet.net Subject: [mg11657] diffusion equation in two dimensions Dear Colleagues, I am trying to solve a two dimensional diffusion equation with a coordiante dependent diffusion tensor. Therefore, I wonder if there is any Mathematica package available which might be of any help. Any advise sent to dimiter@shemesh.chem.purdue.edu will be greatly appreciated. Regards, Dimiter Petsev