Asym =

If I could argue ro me all methods fail. This matrix do not have two eigenvalues (or one with multiplicity 2). It has just one (0) with multiplicity 1, and the matrix is not diagonalisable.

It is well known that such matrix (Jordan form with non-zero on upper diagonal) are notoriously difficult and cannot be well factorized by EIG and alike.

I wouldn't try to find an explanation logic behind the values in this specific example, eig with 1 or 2 arguments simply use different algorithm, IIRC respectively qr algorithm and algorithm based on Schur decomposition. There is no reason to call eig with eye() as second argument as general rule.