Lets add a warning in documentation of these routines regarding device synchronization

However, cuSolver only provides the eigenvalue solver of a symmetric (Hermitian) matrix but does not the one of a general matrix.

Hi @takagi @ev-br @andfoy I could really pick your brains here regarding the general-matrix eigensolver. Why isn't it possible to rewrite the algorithms such that you generate a Hermitian matrix? What's special here? (Context: On the cuSOLVER side, I learned that there's great hesitation in adding the general solver because there's no serious use case. A lot of eigvals calls were done, in our opinion, only because people either didn't know eigvalsh exists or didn't know their matrix is Hermitian/symmetric by construction. Also, svd might help for a lot of use cases (#6359 (comment)). We would love to know what's missing in this understanding.)

Thanks @leofang for letting my head up. As for numpy.roots, the roots of a polynomial is found as the eigenvalues of its companion matrix, and the matrix is not symmetric/Hermitian.

https://en.m.wikipedia.org/wiki/Companion_matrix

I suppose we need eigenvalues themselves, not just decomposition, so svd may not work.

However, yes, we might use another algorithm for root finding on GPU that does not use eigenvalues.

https://hal.science/hal-02129742/file/880a5bc7-2a3d-4a66-a539-9755508a949b-author.pdf

Also I’ll look into other lines that use eigvals...