Defining Sparse Matrices A matrix is a two-dimensional array defined by rows and columns. A sparse matrix specifically has most of its entries equal to zero, meaning non-zero elements are relatively few. This definition sets the stage for understanding how sparse matrices differ from dense matrices in structure and composition.
Efficiency Through Zero Exclusion Eliminating the storage of zeros in a sparse matrix greatly reduces memory usage. Focusing only on non-zero elements minimizes computational overhead during data processing. This efficiency in both memory and computing time illustrates the practical advantage of sparse matrix utilization.
Compact Representations Using Arrays and Linked Lists Sparse matrices can be represented using an array format that stores the row, column, and value of each non-zero element. Alternatively, a linked list structure uses nodes containing the row, column, non-zero value, and a pointer to the next node. Both methods streamline data handling by capturing only the essential information and avoiding unnecessary storage of zeros.