Choice of conjugation in complex inner product

[lezcano]

vecdot is defined for complex vectors as $\langle x, y \rangle = \sum_i x_i \overline{y_i}$. This can be written as $\langle x, y \rangle = y^H x$ (note how the order of the parameters is swapped).

In PyTorch we define it as $\langle x, y \rangle = x^H y$. This notation is more common in physics, while the previous notation is more common in complex geometry. For a short discussion see this wikipedia page.

I would argue that numerical libraries are more targeted to physics people than to pure math people, so perhaps it'd be better to stick with the physics notation?

[asmeurer]

I've transferred this issue to the array-api repo.

[kgryte]

What is the ask here? Is this just a question about updating the docs or something else?

[lezcano]

It's a question about the definition of vecdot for complex inputs in the array API (should it conjugate the first or the second input?)

[kgryte]

This issue has been closed by #723. During the workgroup meeting on 30 Nov, we discussed this issue and consensus was to align the definition of the complex inner product with PyTorch and NumPy, as described in the OP. The definition previously in the spec was an oversight, and the changes have been backported to the 2022 revision of the API standard.