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given a complex vector space with a hermitian inner product, how is thecosine of the angle between two vectorsdefined?

I tried to follow a similar reasoning as in the real case and I got the following:

[tex]cos(\theta)=\mathcal{R}e \frac{ \left\langle u,v\right\rangle}{\left\|u\right\| \left\|v\right\|}[/tex]

Does this make any sense?

If that is correct it means two vectors are perpendicular whenever thereal partof their hermitian inner product is zero.

Again, if that is correct, how can we compute theprojectionof one vector onto another?

Thanks!

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# Perpendicularity on complex vector space

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