A Gram–Schmidt R entry

MediumLinear Algebra~5m

Form the QR decomposition $A=QR$ of $A=\begin{pmatrix} 3 & 5 \\ 4 & 0 \end{pmatrix}$ (columns $a_1=(3,4)$ , $a_2=(5,0)$ ) using Gram–Schmidt with $R$ having a positive diagonal. What is the entry $R_{22}$ ? (to 4 decimals)

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Normalize $a_1$ to $q_1$ , then compute $R_{12}=q_1\cdot a_2$ .
$R_{22}$ is the length of $a_2 - R_{12}q_1$ , the part of $a_2$ orthogonal to $q_1$ .

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4 (± 0.001)

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Asked at: Citadel, Two Sigma

A Gram–Schmidt R entry

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