Past exam of the algebra and analysis II for mathematics and philosophy course of the University of Oxford / 2013 / 2 / b / ii

Table of contents
- Solution ii

Solution

In part (i), set every

b_{i} = 1

. Its squared norm is

n

n i = 1 \sum n a_{i}^{2} \geq (i = 1 \sum n a_{i})^{2} .

The equality condition is

a_{1} = \dots = a_{n}

, because

a

must be a scalar multiple of

(1, \dots, 1)

.

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