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 From the Mathematica 5.2 docs (suposedly outdated) I also know that e.g. the following works (and still works in 8) Eigenvalues[matrix, 2, Method-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