Is defective eigenvalue an acceptable term that is used often? By a defective eigenvalue, I mean an eigenvalue whose geometric multiplicity is strictly less than its algebraic multiplicity.

I have seen it used occasionally but not enough to be sure that it is an “official” terminology in the sense that defective matrix is definitely an official terminology.


1 Answer 1


It is not very common notation, simply because the concept of a defective eigenvalue doesn't need to be used very often. If I were using it in a paper, I would define the term first.

Another possible term is "deficient eigenvalue", which is the first thing that came to mind for me - but at least by the Google hits metric it is less popular.

The advantage of "defective eigenvalue" is that it corresponds to "defective matrix", but the advantage of "deficient eigenvalue" is that you can talk about the "deficiency of the eigenvalue" - the amount by which the algebraic multiplicity is less than the geometric. I don't think either term is established enough that you can't pick the one you like better.


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