We have already seen numerous examples of arrays and matrices being the essential entities in many aspects of numerical computing. So far we have represented arrays with the NumPy ndarray data structure, which is a heterogeneous representation that stores all the elements of the array that it represents. In many cases, this is the most efficient way to represent an object such as a vector, matrix, or a higher-dimensional array. However, notable exceptions are matrices where most of the elements are zeros. Such matrices are known as sparse matrices, and they occur in many applications, for example, in connection networks (such as circuits) and in large algebraic equation systems that arise, for example, when solving partial differential equations (see Chapter 11 for examples).