A sparse matrix is a one in which the majority of the values are zero. The proportion of zero elements to non-zero elements is referred to as the sparsity of the matrix. The opposite of a sparse matrix, in which the majority of its values are non-zero, is called a dense matrix.
Sparse matrices are used by scientists and engineers when solving partial differential equations. For example, a measurement of a matrix's sparsity can be useful when developing theories about the connectivity of computer networks. When using large sparse matrices in a computer program, it is important to optimize the data structures and algorithms to take advantage of the fact that most of the values will be zero.
Sparse matrix example
Here is an example of a 4 x 4 matrix containing 12 zero values and 4 non-zero values, giving it a sparsity of 3:
[[5, 0, 0, 0],
[0, 11, 0, 0],
[0, 0, 25, 0],
[0, 0, 0, 7]]