Eigensystem ordering

*To*: mathgroup at yoda.physics.unc.edu (Mathematica User's Group)*Subject*: Eigensystem ordering*From*: Keith Clay <clay at galileo.phys.washington.edu>*Date*: Tue, 21 Sep 93 9:27:57 MDT

The following question came to me from two fellow Mathematica users, and I cannot find an answer in any of the standard literature: > When you call Eigensystem[m], you get a result of the form: > > { n-vector, {vector1, vector2, ... , vector_n}} > > Q: Does the ith Eigenvalue in n-vector ALWAYS correspond to the ith > Eigenvector in the list? It usually does, but we want to know if this > can always be assumed. ONE OF US THINKS THIS SHOULD BE TRUE, ANOTHER > THINKS THEY HAVE SEEN A CASE TO THE CONTRARY. In other words, can we be sure this quantity is always zero Eigensystem[m][[1,i]]*Eigensystem[m][[2,i]] - m.Eigensystem[m][[2,i]] (with the same i used for the eigenvector and eigenvalue)? Has anyone else seen a case to the contrary? (Page 664 of The Book says that this is true for one matrix, for i=1. Searching for exceptions has turned up none, but these people are looking for certainty.) It would certainly seem absurd to report the results any other way, but I can't find any guarantees or details of how the output is put together. Thanks. ------------------------------------------------------------------------ Keith Clay Department of Physics, FM-15 (clay at galileo.phys.washington.edu) University of Washington ( -or- clay at phys.washington.edu ) Seattle, WA 98195