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MathGroup Archive 2010

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Documentation of Eigenvalues[], Eigensystem[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114007] Documentation of Eigenvalues[], Eigensystem[]
  • From: Michael Weyrauch <michael.weyrauch at gmx.de>
  • Date: Sat, 20 Nov 2010 18:23:46 -0500 (EST)

Hello

    it appears that the documentation of some "classic" functions
like Eigenvalues[] and Eigensystem[] is rather incomplete in
Mathematica 8 (and 7 and 6). Under the Options section one only finds 
the options Cubics and Quartics.

In one example given in "Possible issues" section
one realizes that there is also a "Method" option with rather obscurely
defined suboptions like "Shift". From the Mathematica 5.2 docs 
(suposedly outdated) I also know that e.g. the following works (and 
still works in 8)

Eigenvalues[matrix, 2, Method->{"Arnoldi", StartingVector-> vector}]

and it is indeed sometimes very time efficient to be able to give
a starting vector to the Arnoldi iteration procedure. Unfortunately all 
these possibilities are not documented in more recent
versions of Mathematica, which I find very odd given that e.g. rather
extremely special functions like NVCCCompiler[] are documented with an
extensive list of even the most outlandish options (I guess).

Does anybody know of a comprehensive list of "Options" available
for some "classic" functions like Eigenvalues etc.? (For the Frontend we
even have an "Options inspector". Maybe there is also one for other 
functions??)

Michael Weyrauch


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