Do we need real / cong / imag?

[rveltz]

Do we need the above functions in the interface or the interface provides them already albeit undirectly?

[Jutho]

I don't know if we need these? The goal of VectorInterface was to provide minimal interface for standard linear algebra techniques (very much inspired by and perhaps as a consequence limited to Krylov methods). I haven't needed any of those methods in these cases. This doesn't mean that most types of vectors that support this minimal interface will also have a notion and therefore an implementation of real/conj/imag, but whether we need to impose this as part of the minimal interface is not clear to me. In particular, unlike the other methods in VectorInterface, these methods only make sense with respect to a chosen basis of the vector space. And while I do not want to be too pedantic and agree that whenever you store data in a computer, you have chosen a basis, I do think this is an important difference.

As a bit of side information: KrylovKit actually supports reinterpreting "vectors" that live in a complex vector space as vectors in a real vector space. However, this does not require taking real and imaginary parts separately. All that is required is to only admin real linear combinations (i.e. add!! with real scalars, which definitely works if even complex scalars are supported) as well as redefining the inner product to only consider the real part of the complex-valued inner product.

[rveltz]

I see how it is done in KK now. Thank you!