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Year 2 of the mathematics and statistics course of the University of Oxford

Probability, statistics and options II course of the University of Oxford

Past exam of the Probability, statistics and options II course of the University of Oxford

2010

Expand using the <inner product>. The two cross terms cancel:
$$
\|x+y\|^2=\|x\|^2+\|y\|^2+2\Re\langle x,y\rangle,\qquad\|x-y\|^2=\|x\|^2+\|y\|^2-2\Re\langle x,y\rangle.
$$
Adding proves $\boxed{\|x-y\|^2+\|x+y\|^2=2(\|x\|^2+\|y\|^2)}$, for real or complex inner products.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / P / P3 / b / Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / P / P3 / b / Solution

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Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / P / P3 / b / Solution

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