orthonormal version of Eigensystem?
- To: firstname.lastname@example.org
- Subject: [mg11620] orthonormal version of Eigensystem?
- From: email@example.com (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 firstname.lastname@example.org 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: email@example.com (Dimiter Petsev) To: firstname.lastname@example.org 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 email@example.com will be greatly appreciated. Regards, Dimiter Petsev