Where does “eigenbundle” come from?
eigenbundle (English) comes from English eigen-, from German eigen, from Middle High German eigen, from Old High German eigan, from Proto-West Germanic aigan, from Proto-Germanic *aiganą, from Proto-Indo-European h₂eh₂óyḱe, from Proto-Indo-European h₂eyḱ- — to possess, to own.
eigenbundle (English): Given a section s of an endomorphism bundle Hom(E, E) and a function f: X → R, an eigenbundle is the result of taking the fiber over a point x ∈ X to be the f(x)-eigenspace of the linear map s(x): E'x → E'x
Definitions
- Given a section s of an endomorphism bundle Hom(E, E) and a function f: X → R, an eigenbundle is the result of taking the fiber over a point x ∈ X to be the f(x)-eigenspace of the linear map s(x): E'x → E'x
Ancestry of “eigenbundle”, step by step
| Step | Language | Word | Meaning |
|---|---|---|---|
| 1 | English | eigen- | — |
| 2 | German | eigen | own, peculiar or private to someone,... |
| 3 | Middle High German | eigen | — |
| 4 | Old High German | eigan | own; possession, property |
| 5 | Proto-West Germanic | aigan | to possess, to own, to have; own |
| 6 | Proto-Germanic | *aiganą | — |
| 7 | Proto-Indo-European | h₂eh₂óyḱe | to possess, to own |
| 8 | Proto-Indo-European | h₂eyḱ- | to possess, to own |