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Year 3 of the mathematics course of the University of Oxford

Analysis course of the University of Oxford

Past exam of the analysis course of the University of Oxford

2007

Expand both squared <norms> using sesquilinearity and <conjugate symmetry>. Their mixed terms $\langle u,v\rangle+\langle v,u\rangle$ appear with opposite signs and cancel. Hence
$$
\boxed{\|u+v\|^2+\|u-v\|^2=2\|u\|^2+2\|v\|^2,}
$$
the <parallelogram identity>.

Solution

Past exam of the analysis course of the University of Oxford / 2007 / B / 5 / a / Solution

Past exam of the analysis course of the University of Oxford / 2007 / B / 5 / a / Solution

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Past exam of the analysis course of the University of Oxford / 2007 / B / 5 / a / Solution

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