Sparse matrices

Sparse matrices are matrices that contain a significant number of zero elements. In contrast to dense matrices, where most of the elements are non-zero, sparse matrices are characterized by having a high proportion of zero entries. This sparsity can arise in many applications, particularly in scientific computing, graph theory, optimization problems, and machine learning. ### Characteristics of Sparse Matrices: 1. **Storage Efficiency**: Because many elements are zero, sparse matrices can be stored more efficiently than dense matrices.