Implement hermitian conjugate utilities

[gautierronan]

x.T.conj() -> x.H
x.mT.conj() -> x.mH

Similar to pytorch behavior, very useful for dealing with complex arrays.

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[jakevdp]

Hi - typically for array attributes and properties we've followed NumPy and/or the Python array API standard in order to minimize the cognitive overhead for people switching between standard Python array syntax. NumPy does not have .H and .mH, and this idea has been proposed and rejected on several occasions (see e.g. numpy/numpy#8882 and links within). In the Array API standard, the idea is being considered (data-apis/array-api#555), but is not yet part of the standard, though it appears to be on the draft roadmap for a future revision: data-apis/array-api#643.

That's not to say that we shouldn't add this, but it means there is a higher bar before we consider adding such syntax. Some of the concerns in the above discussions don't really apply to JAX, particularly in JIT-compiled mode where the hermitian transpose operation can be optimized away. If the array API standard adds this, we should ensure that JAX's definition is compliant, otherwise we might be facing a rather painful deprecation process for adjusting the syntax in the near future.

With all that in mind, I think we should hold off on this for now – what do you think?

[gautierronan]

Thanks for your detailed answer. My point of view on the matter is that this feature is:

1. very simple to add and maintain,
2. very practical for users who work on complex arrays regularly (I personally use x.conj().T tens of times every day),
3. already implemented in pytorch (although they are much less compliant with the numpy API of course).

That being said, your arguments are also very sound. I'll let you guys decide, but I'm very much in favor of the feature :)