The most recent version of cusolver seems to support a new GPU accelerated algorithm for eigendecomposition of general nonsymmetric matrices (https://docs.nvidia.com/cuda/cusolver/index.html?highlight=eigendecomposition#cusolverdnxgeev).

According to one of the authors, we could expect a several-fold speedup over the existing MAGMA GPU implementation (cupy/cupy#6359 (comment)). This would be a very welcome new feature for jax.