$\langle v,w\rangle \cdot \langle w,v\rangle = |\langle v,w\rangle|^2$ proof?

73 Views Asked by At

I can't seem to prove this identity I have been given:

$\langle v,w\rangle \cdot \langle w,v\rangle = |\langle v,w\rangle|^2$

Could you please outline how to go about it?

1

There are 1 best solutions below

2
On BEST ANSWER

Just from the definition of the hermitian product

$$\overline{\langle v,w\rangle}=\langle w,v\rangle$$

and for $z\in\Bbb C$, $z\overline z=\vert z\vert^2$.