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Exercise 1.12.1

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Take derivative of the column norm w.r.t. $v_{1}$ , we have

$\frac{d}{d v_{1}} = - 2 (a - v_{1} u_{1}) u_{1} - 2 (b - v_{1} u_{2}) u_{2}$ , let it equal to 0, we have $(u_{1}^{2} + u_{2}^{2}) v_{1} = a u_{1} + b u_{2}$ , which in vector notation we have $u^{T} u v_{1} = u^{T} a_{1}$ where $a_{1}$ is the column 1 of $A$ .

niuers

2020-03-20 00:00

Exercise 1.12.1

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