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  "body": "\n## Summary\n\nA Hadamard matrix is a square [[matrix|0VD9ZSWWJG]] with entries $\\pm 1$ whose rows are pairwise orthogonal.\nTheir determinant has absolute value $n^{n/2}$, the largest possible for a real $n \\times n$ matrix with entries in $[-1, 1]$.\nHadamard matrices give error-correcting codes, block designs and experimental designs.\nThe node [[Hadamard matrix|DM59GHSMAJ]] gives the precise definition.\n\n## Explanations\n\n### L1 human\n\nTake a square grid of plus and minus signs.\nIt is a Hadamard matrix if any two rows agree in exactly half of the places and disagree in the other half.\nThe smallest interesting one is the $2 \\times 2$ grid with rows $+\\,+$ and $+\\,-$.\nRepeating this pattern in blocks gives Hadamard matrices of sizes $4, 8, 16$ and so on.\n",
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