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  "body": "\n## Definition\n\nLet $A$ be an $m \\times n$ [[matrix|0VD9ZSWWJG]], and let $\\operatorname{nnz}(A)$ be the number of its nonzero entries.\nThe matrix $A$ is *sparse* when $\\operatorname{nnz}(A)$ is small compared with $mn$, so that it pays to store and process only the nonzero entries.\nFor a family of $n \\times n$ matrices with $n$ growing, a common precise form of this condition is $\\operatorname{nnz}(A) = O(n)$.\n\n## Remarks\n\nThe notion has no fixed threshold; it depends on the size of the matrix and on the algorithms in use.\nThe *density* of $A$ is $\\operatorname{nnz}(A) / (mn)$, and a matrix that is not sparse is called *dense*.\nExample: the $n \\times n$ [[tridiagonal matrix|DARX1KZRHZ]] with $2$ on the diagonal and $-1$ beside it has $3n - 2$ nonzero entries, which is $O(n)$, so the family is sparse.\nNon-example: the $n \\times n$ matrix with all entries $1$ has $n^2$ nonzero entries, so it is dense.\nCommon storage formats are the coordinate list and the compressed sparse row format.\n",
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