Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
- To: mathgroup at smc.vnet.net
- Subject: [mg21335] Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
- From: sidles at u.washington.edu (John A. Sidles)
- Date: Sun, 26 Dec 1999 01:26:13 -0500 (EST)
- Organization: University of Washington, Seattle
- References: <firstname.lastname@example.org> <email@example.com> <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
In article <83ncc5$5ph$4 at dragonfly.wolfram.com>, Kevin J. McCann <kevinmccann at Home.com> wrote: >Well it looks like Ingolf has got himself a winner here. I tried it on my >W98 system and Commands 1,2,3 crash the kernel. Further, command 1 followed >by repeated execution of the Eigensystem command gives different results >each time. > >Kevin Just to be fair, you gotta read the Eigensystem documentation with the care of a tax lawyer! As Mathematica support staff will confirm, the following behaviors are all legal for Eigensystem, are *not* regarded as bugs by Wolfram Research, and must be respected by anyone who wants to write reliable code: Eigensystem[(a general Hermitian matrix)] => eigenvectors which are (1) complex (2) non-orthonormal (3) different every time Eigensystem is called (4) sensitive to least-significant bits in the input. Eigensystem *does* guarantee that the returned eigenvectors will be complete; this is consistent with the above behaviors. As is well known, it a well-posed numerical problem to calculate the real orthonormal eigenvectors of a general Hermitian matrix, and Eigensystem *usually* does so, but does sporadically return eigenvectors with the above -- more general -- characteristics; this is just a "feature" of life in the Mathematica world. I have no complaints about the above, but I do think the Eigensystem documentation might reasonably be revised to be a little more forthcoming about these behaviors, which over the years have taken so many users by surprise.