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Documentation of Eigenvalues[], Eigensystem[]

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


    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(suposedly outdated) I also know that e.g. the following works (and 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 

Michael Weyrauch

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