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  "body": "\n## Summary\n\nA Euclidean distance matrix is a square matrix whose entries are the squared distances between some points of a Euclidean space.\nIt records the whole shape of a finite point set up to isometry.\n[[Schoenberg's criterion|4B0R70F4VE]] recognizes these matrices through a [[positive semidefinite|01MMVW8CKC]] condition, which links [[distance geometry|HPW5F0GQ4B]] with linear algebra.\nThey are used in multidimensional scaling, molecular conformation and sensor localization.\n\n## Explanations\n\n### L1 human\n\nTake a few points, number them, and write the square of the distance from point $i$ to point $j$ in row $i$ and column $j$.\nThe table you get is a Euclidean distance matrix.\nIt is symmetric with zeros on the diagonal.\nFor the points $0$, $1$ and $3$ on a line, the table has rows $(0, 1, 9)$, $(1, 0, 4)$ and $(9, 4, 0)$.\nThe hard question is the reverse one: given such a table, do points exist that produce it?\n",
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