Sparse matrices can be useful for computing large-scale applications that dense matrices cannot handle. One such application involves solving partial differential equations by using the finite element method. The finite element method is one method of solving partial differential equations (PDEs).
Sparse matrix is a matrix which contains very few non-zero elements. When a sparse matrix is represented with a 2-dimensional array, we waste a lot of space to represent that matrix. For example, a matrix of size 100 X 100 containing only 10 non-zero elements.
Application of sparse matrices is in data structures and computer programming.