The eigen- prefix is used to describe something which is “the same” before and after a transformation. e.g. the eigenvector of a matrix is a vector which still points in the same direction after multiplying by the matrix (scaled by its eigenvalue). What exactly is the transformation going on here?
eigen comes from Germanic languages such as German and Dutch where it means own, particular to, etc.
Mijn eigen auto -> My own car.
Mijn eigenwaarde/eigendunk -> My self-esteem
So, the prefix eigen- does not imply a transformation. Though, I agree that it is confusing in CS to use this prefix, since non-native speakers immediately associate it with eigenvalues/vectors.
The term “singleton class” that the article briefly mentions is actually Ruby’s official term for this concept. Ruby’s standard library defines the Object#singleton_class method; you can use .singleton_class in place of .eigenclass in all the article’s examples. Perhaps this potential confusion is the reason the Ruby team chose “singleton class” over “eigenclass”.
Thank you for your comment.
Eigen means “own” in German. So “eigenclass” means “owned class” (as this anonymous class is owned by its defined class).
Etymologically speaking, the “eigen-”-prefix was used by David Hilbert to describe that the value/vector is inherent to the thing. To confuse things a little, “eigen” is a pretty versatile word in german: https://www.dict.cc/?s=eigen
Hilbert probably used in the sense of “possessive”, “inherent”, “in-built”. In that sense, which is not focused on the transformation, “eigenclass” is rather similar.
(loosely taken and translated from: http://faql.de/etymologie.html#eigen)