Semantics and Help Page of "eye()" needs Clarification

[rdbyk]

What is eye()? A look at the corresponding help page reveals:

...
eye() produces a identity matrix with undefined dimensions. Dimensions will be defined when this identity matrix is added to a matrix with fixed dimensions.
...

Now, based on this knowledge, try to explain why the following results are thoroughly consistent ...

--> diag(eye())
 ans  =
    []

--> sum(eye())
 ans  =
   1.

--> 1/eye()
 ans  =
   1.

--> eye()^(-1)
 ans  =
eye *

   1.

--> 1./eye()
 ans  =
eye *

   1.

Even after reading the help page of eye and analysing the above results, there remains one question:

What is eye()?

It is obvious, that a complete definition for the semantics of eye() is needed asap! Don't you agree?