Suppose you have a data matrix comprised of several stock options over a set period of time. How do you choose the optimal collection of stocks such that you maximize your returns for a given level of risk? What Markowitz found was an elegant equation.
What we realized rather quickly is there does not exist a closed form solution to this problem. Instead we use the tried and tested linear approximation. By transforming this problem into Matrix multiplication, we are able to quickly and (with desired accuracy) approximate the optimal solution, using only linear algebra.