Matrix processing is a heavily used technique in communications, radar, medical imaging, and many other applications. This is particularly prevalent in systems with many antennas and performing multiple input, multiple output (MIMO) processing. In 5G wireless, for example, QR decomposition (QRD) is used in both MIMO processing and amplifier digital predistortion adaptation. In radar, QRD is used in space–time adaptive processing (STAP) and can be used to extract signals well below the noise floor. This chapter has more math than most. These functions are usually already available as library functions for high performance CPUs, GPUs, and FPGAs.