A large number of matrix techniques and theories were developed in the past few decades to address the problems of partial differential equations, which arguably shaped the current era of numerical linear algebra. Its main use lies in solving linear systems and eigenvalue problems, which constitute the major challenges in a large number of scientific and engineering applications. On the other hand, the well developed matrix techniques can be exploited in many scenarios, where the link between the application and its linear algebra content may sometimes be subtle. We discuss in this talk five such instances, all of which can be translated into matrix problems, and existing matrix techniques can be adapted or novel methods can be developed to solve the original applications. They include performing dimension reductions to a high dimensional data set, constructing nearest neighbors graphs for high dimensional data, identifying communities in a network system, measuring the connectivity of a pair of nodes in a graph, and sampling points from a multivariate normal distribution. These examples indicate that numerical linear algebra plays an important role in emerging areas such as data mining, and that it provides indispensable tools for computational and scientific applications.