matvis simulates radio interferometric visibilities at the necessary scale with both CPU and GPU implementations. It is matrix-based and applicable to wide field-of-view instruments such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA), as it does not make any approximations of the visibility integral (such as the flat-sky approximation). The only approximation made is that the sky is a collection of point sources, which is valid for sky models that intrinsically consist of point-sources, but is an approximation for diffuse sky models. The matvix matrix-based algorithm is fast and scales well to large numbers of antennas. The code supports both CPU and GPU implementations as drop-in replacements for each other and also supports both dense and sparse sky models.