As in, I cannot simply sign up with my own personal identifiers (email, phone, etc.) but need to participate in a google auth or FB auth mechanism ?
I found it hard to believe - is this, indeed, the case ?
It's a weird process and not particularly user friendly (passkey accounts are tied to a specific passkey and can't have additional ones added, so you need to create a new account if you, say, migrate from one hardware key to another). Hopefully they improve the process before passkey support goes out of beta.
Is your approach specific to the case where the matrix fits inside cache, but the memory footprint of the basis causes performance issues? Most of the communication-avoiding Krylov works I've seen, e.g [0,1] seem to assume that if the matrix fits, so will its basis, and so end up doing some partitioning row-wise for the 'large matrix' case; I'm curious what your application is.
[0] https://www2.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-..., e.g. page 25. [1] https://www2.eecs.berkeley.edu/Pubs/TechRpts/2015/EECS-2015-...