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Exercise 1.8.3

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When $x^{T} v_{1} = 0$ , it means ${(c_{1} v_{1} + \dots + c_{n} v_{n})}^{T} v_{1} = c_{1} = 0$ . Under such condition, we have

$R (x) = \frac{λ_{2} c_{2}^{2} + \dots + λ_{n} c_{n}^{2}}{c_{2}^{2} + \dots + c_{n}^{2}}$ , we see that $R (x)$ is maximized when $c_{2} = 1$ and $c_{1} = c_{3} = \dots = c_{n} = 0$ , and the maximal value is $λ_{2}$ .

niuers

2020-03-20 00:00

Exercise 1.8.3

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