I noticed that in the question Request for clarification of Eigensystem::eivn message the error message
Eigensystem::eivn: Incorrect number 2 of eigenvectors for eigenvalue Root[<<14>>+(<<1>>) #1^6+(104.294 r^4+134.491 a r^4+22564.8 a c r^4-0.497321 n r^4) #1^7+(21.6958 r^2-0.0208333 n r^2) #1^8+1. #1^9&,1] with multiplicity 1.
was ruled as bug of version 9. I have version 10.0.2 and I'm getting the same message for another matrix, this one with no symbolic objects in the entries. It's a pretty big beast, and the reason I do not want to use a numerical solution like
Eigenvectors[N[matrix]] is related to another question I asked some time ago: What if do NOT want Mathematica to normalize eigenvectors with Eigenvectors[N[matrix]]?. If asked, I can post the matrix in question in an EDIT, but my question is actually more general: how does one avoid the error
Eigensystem::eivn: Incorrect number X of eigenvectors for eigenvalue Y with multiplicity Z.
and how come it shows up. It is to me unclear if there is a way of fixing this, if it's a bug, if there are ways to work around this. The problem is that Mathematica is not able to match eigenvalues with multiplicity Z to a number Z of eigenvectors, but he finds a different number X which is higher than Z in all cases I've seen. Might this have to do with how Mathematica deals with the case of having more eigenvalues than independent eigenvectors, namely by using zero vectors? Could one solve this by computing first the eignvalues and then for each one find the corresponding set of eigenvectors via another route that is not
Eigenvectors[matrix], or is it just a waste of time?