fresh_42 said:
To own is then even stronger than to possess.
As verbs, own is abstract, and possesses is physical.
Is 'sehr eigenes arm' = 'his own arm' not correct?
There are certainly relations, as Eigentum is ownership, but Eigenschaft is property,
and Eigenheit habit.
In each of those words, 'eigen' contributes some sense of 'own', and each could be anglicized by 'own' prepended to a suffix: 'eigentum' ≈ 'owndom', 'eigenschaft' ≈ 'ownship', 'eigenheit' ≈ 'ownhood'.
These all show that eigen is far more variable than own or proper is.
I would own that contention to be founded on little more than an impropriation to yourself of a declaratory fiat on the matter.
And it has a clear tendency towards a special property which makes it best fit for eigenvalues.
I wouldn't disagree with the claim that it's a good choice.
A vector doesn't own his eigenvalue, nor is it a proper value.
In English, we wouldn't say of a thing that it owns (verb) anything, but we could refer to its own (adjective) characteristic value (not 'his own', because mathematical objects, quite properly (in the sense of 'rightfully') in my (own) opinion, don't have gender in English).
This would immediately raise the question about improper values.
Not if we don't improperly (i.e incorrectly in this instance) use the word 'proper' intransitively, and say instead that the value 'is proper to it', meaning 'belongs to it' or (more reachingly) 'is characteristic of it'.
These might be true, but words change their meaning over centuries. You cannot apply their original meaning one-to-one.
Of course that's true; however, ancestor languages being static, except perhaps when a previously lost ancient document is discovered, it is not wrong for us to consult the meanings of the ancient root words when constructing words for newly discovered characteristics.