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CholeskyDecomposition[{{25, 15, -5}, {15, 18, 0}, {-5, 0, 11}}]
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chol[A_] :=
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Module[{L},
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L[k_, k_] := L[k, k] = Sqrt[A[[k, k]] - Sum[L[k, j]^2, {j, 1, k-1}]];
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L[i_, k_] := L[i, k] = L[k, k]^-1 (A[[i, k]] - Sum[L[i, j] L[k, j], {j, 1, k-1}]);
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PadRight[Table[L[i, j], {i, Length[A]}, {j, i}]]
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]
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