Fixing `linalg.eig` dtype instability

Hi Team,

gh-26214 proposes to immediately patch the dtype instability in scipy.linalg.eig so the output dtype of the eigenvectors is always complex rather than being value-dependent.

The instability was maintained for backward compatibility, so please join the discussion if there are concerns with this changed.

Matt

+1 for making both eigenvalues and eigenvectors always have a complex dtype.

The reasoning from the matching numpy change I think fully applies to the SciPy’s linalg.eig variant.
Also I think the conclusion from effect of the numpy change is that the downstream damage is less than expected, and that the backwards-incompatible change is well worth it.

Cheers,
Evgeni