  This survey highlights the recent advances in algorithms for numerical linear
algebra that have come from the technique of linear sketching, whereby given a
matrix, one first compresses it to a much smaller matrix by multiplying it by a
(usually) random matrix with certain properties. Much of the expensive
computation can then be performed on the smaller matrix, thereby accelerating
the solution for the original problem. In this survey we consider least squares
as well as robust regression problems, low rank approximation, and graph
sparsification. We also discuss a number of variants of these problems.
Finally, we discuss the limitations of sketching methods.
