Bug or feature in Eigensystem[]?
- To: mathgroup@smc.vnet.net
- Subject: [mg11691] Bug or feature in Eigensystem[]?
- From: sidles@u.washington.edu (John Sidles)
- Date: Sat, 21 Mar 1998 18:35:24 -0500
- Organization: University of Washington, Seattle
Dear Mathematica users
Usually, given a real symmetric matrix, Eigensystem[] returns what
anyone would expect: real eigenvectors. But about one time in a
thousand (for my example matrices, see below), it turns out that
Eigensystem[] returns complex eigenvectors.
This behavior occurs sporadically even for real numerical matrices that
are nonsingular, symmetric, and diagonally dominant, with sparse
off-diagonal entries -- these are exactly the matrices that
Eigensystem[] *should* handle most easily. The matrices need not be
large -- my examples are dimension {18,18}.
Because of this bug -- or is it a "feature"? -- better call it a
"behavior" -- there seems to be no reliable way on my platform (a Mac
PowerBook G3) to compute the real orthonormal eigenvectors of a real
symmetric matrix -- so I am quite distressed & would welcome
suggestions. I would particularly appreciate it if other people would
try to reproduce this behavior on their platforms.
I have posted a notebook which duscusses this behavior at:
ftp://ftp.u.washington.edu/public/sidles/EigenBug.nb
It does not seem to be discussed on the Mathematica support page:
http://www.mathematica.com/support/Math
but it *should* be discussed there -- this behavior can really can
really mess up a quantum mechanical calculation. And even if you know
it is present, it is not clear how to fix it. Advice is welcome.
Thanks ... JAS
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John A. Sidles, Ph.D. email: sidles@u.washington.edu
Associate Professor phone: (206) 543-3690 Department of
Orthopaedics FAX: (206) 685-3139 Box 356500, School of
Medicine PAGE: (206) 989-9462 (to page me, University of
Washington dial, await "beep", enter Seattle WA
98195-6500 USA phone number, press "#")
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