Sparse matrix

Remarks

The notion has no fixed threshold; it depends on the size of the matrix and on the algorithms in use. The density of $A$ is $\operatorname{nnz}(A) / (mn)$, and a matrix that is not sparse is called dense. Example: the $n \times n$ tridiagonal matrix with $2$ on the diagonal and $-1$ beside it has $3n - 2$ nonzero entries, which is $O(n)$, so the family is sparse. Non-example: the $n \times n$ matrix with all entries $1$ has $n^2$ nonzero entries, so it is dense. Common storage formats are the coordinate list and the compressed sparse row format.