The use of "eigen" here seems to have stretched too far beyond its original meaning in mathematics, and in German more generally. In German, "eigen" means "own" like "my own idea." In mathematics, "eigenvalue" is a certain numeric value associated to a matrix or linear operator, which is independent of various representations of that matrix or operator. In that sense, the number is the operator's "own" value, in the sense of it being an invariant and characteristic property of the underlying concept, rather than arising from how it's viewed in a particular frame.

The author borrows the prefix from the "eigenquestions" article linked therein, where that author defines it as

> "Eigenquestion" is a made-up-word that borrows from the linear algebra concept of eigenvectors (mathematically: represents the "most discriminating vector in a multidimensional space"). ... For a simplistic definition, the eigenquestion is the question where, if answered, it likely answers the subsequent questions as well. Great framing starts by searching for the most discriminating question of a set — the eigenquestion.

But the "most discriminating vector" idea is not really what an eigenvector is. It can be roughly thought of as that in some senses, like principal component analysis or SVD, where the term has been used to refer to a particular vector space basis formed of eigenvectors (e.g., "eigenfaces"). But in this context they authors are simplifying this to just "the most important question." The use of the fancy math jargon doesn't seem to add anything beyond this. It feels like a kind of faux intellectualism that I have learned to dislike (despite having a math PhD myself!) after hearing too many tech bro types abuse math terms beyond recognition.