Confirmed.  I changed the Summary to reflect that this is merely a Matlab Compatibility difference.  In the cases I tried, Matlab always returns a vector of all NaNs whenever the input contains even one Inf or NaN value.

We could choose to make Octave do the same thing.  The code is in the directory liboctave/numeric/ and in the files EIG.cc and fEIG.cc.  There are four init() routines in each file which have a check similar to this one

  if (a.any_element_is_inf_or_nan ())
    (*current_liboctave_error_handler)
      ("EIG: matrix contains Inf or NaN values");

For nonfinite matrices, the result in Matlab is a NaN-vector:

eig ([1, NaN; 0, 1])
ans =

   NaN
   NaN

and

eig ([1, NaN; 0, 1])

ans =

   NaN
   NaN

In Matlab

eig(Inf)
+verbatim+
and
+verbatim+
eig(NaN)
+verbatim+
return NaN. In Octave, the code will instead crash with

> error: EIG: matrix contains Inf or NaN values

This requires to add an additional exception handling layer.