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  "body": "\n## Summary\n\nA Cauchy matrix has entries $1/(x_i - y_j)$ for two lists of numbers $x_1, \\dots, x_m$ and $y_1, \\dots, y_n$ with $x_i \\ne y_j$.\nIts determinant has an explicit product formula, the Cauchy determinant.\nAs a result, a square Cauchy matrix is invertible when the $x_i$ are distinct and the $y_j$ are distinct.\nThe [[Hilbert matrix|2DTWB6F5TA]] is the best known Cauchy matrix.\n\n## Explanations\n\n### L1 human\n\nPick two lists of numbers that share no value.\nFill a table with one over the difference of a number from the first list and a number from the second.\nFor example, with $x = (1, 2)$ and $y = (0, -1)$ one gets $\\begin{pmatrix} 1 \u0026 \\tfrac12 \\\\ \\tfrac12 \u0026 \\tfrac13 \\end{pmatrix}$.\nSuch tables appear in rational interpolation and in coding theory.\nTheir determinants factor completely, much like the Vandermonde determinant.\n",
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