ArrayFire is a GPU matrix library for the rapid development of general purpose GPU (GPGPU) computing applications within C, C++, Fortran, and Python. ArrayFire contains a simple API and provides full GPU compute capability on CUDA and OpenCL capable devices. ArrayFire provides thousands of GPU-tuned functions including linear algebra, convolutions, reductions, and FFTs as well as signal, image, statistics, and graphics libraries. We will further describe how ArrayFire enables development of GPU computing applications and highlight some of its key functionality using examples of how it works in real code.