A Cholesky diagonal entry

MediumLinear Algebra~4m

The symmetric positive-definite matrix $A=\begin{pmatrix} 4 & 6 \\ 6 & 25 \end{pmatrix}$ factors as $A = LL^\top$ with $L$ lower-triangular and positive diagonal. Compute the bottom-right entry $L_{22}$ . (to 4 decimals)

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Match $LL^\top$ to $A$ entry by entry: $L_{11}=\sqrt{4}$ , then $L_{21}=6/L_{11}$ .
$L_{22}=\sqrt{A_{22} - L_{21}^2}=\sqrt{25-9}$ — subtract the earlier column's contribution.

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Asked at: DRW, Two Sigma

A Cholesky diagonal entry

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