Hey Mateusz, good idea to get started on this topic.

but you meant adding these methods to np.linalg directly, right?

Indeed. We want the numpy namespace, and the numpy.fft and numpy.linalg ones, to be compatible with what's in the standard. The numpy.array_api is a much more strict and limited implementation that is primarily useful for testing compliance with the standard and not assuming any "extra" behavior or syntax.

For a reference I'm looking at:

Yep, that's a good place to start. The other place to look at is https://numpy.org/devdocs/reference/array_api.html#table-of-differences-between-numpy-array-api-and-numpy; the "compatible" and "breaking" entries there are the things to add/change.

Thanks @mtsokol!