  Large matrices arise in many machine learning and data analysis applications,
including as representations of datasets, graphs, model weights, and first and
second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an
area which uses randomness to develop improved algorithms for ubiquitous matrix
problems. The area has reached a certain level of maturity; but recent hardware
trends, efforts to incorporate RandNLA algorithms into core numerical
libraries, and advances in machine learning, statistics, and random matrix
theory, have lead to new theoretical and practical challenges. This article
provides a self-contained overview of RandNLA, in light of these developments.
