- #1

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Thanks for any guidance.

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- Thread starter TheOldHag
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- #1

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Thanks for any guidance.

- #2

Office_Shredder

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Can you explain your question in a way that doesn't require having the book?

- #3

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It's not an equality; it is ≤.

2Re< u, v > ≤ 2|<u, v>|

2Re< u, v > ≤ 2|<u, v>|

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- #4

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- #5

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Just plug in ##\mathbf{v}=\alpha \mathbf{u}## and see what happens.

- #6

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|<u, au>| =

| a*u1*comp(u1) + a*u2*comp(u2) + ... + a*uN*comp(uN) | =

| a |u1|^2 + a |u2|^2 + ... + a |uN|^2 |

And from here I have no idea where that is taking me. Similar result form the other side.

- #7

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[itex]|<u, au>|[/itex] =

[itex]\sqrt{(Re <u, au>)^{2} + (Im <u, au>)^{2}}[/itex] =

[itex]\sqrt{(Re \overline{a} <u, u>)^{2} + (Im \overline{a} <u, u>)^{2}}[/itex] =

[itex]\sqrt{(Re \overline{a} \left\|u\right\|^{2})^{2} + (Im \overline{a} \left\|u\right\|^{2})^{2}}[/itex] =

[itex]\sqrt{(Re \overline{a} \left\|u\right\|^{2})^{2}}[/itex] =

[itex]Re \overline{a} \left\|u\right\|^{2}[/itex] =

[itex]Re <u, au>[/itex]

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