Dot Product Notation Clarification

[CantorSet]

The following notation is from the book "Frames and Bases."

Let f and g be vectors in R^{n} with the usual dot product <,>.

Then, what does the notation \left|\left\langle f,g\right\rangle\right|^{2} mean?

Specifically, does it mean \left|\sum^{n}_{i=1}f_{i} g_{i}\right|

or does it mean \left(\sum^{n}_{i=1}f_{i} g_{i}\right)^{2}

 

[lurflurf]

so in such notation <f,g> is the dot product of f and g.
|<f,g>|^2 is the square of the absolute value of that dot product.
Some dot products are always real and the absolute value is redundent.
Other dot products can be complex and the absolute value is needed.

 

[CantorSet]

so in such notation <f,g> is the dot product of f and g.
|<f,g>|^2 is the square of the absolute value of that dot product.
Some dot products are always real and the absolute value is redundent.
Other dot products can be complex and the absolute value is needed.

Thanks for responding. I was thinking that too. But it just seems inconsistent with the notation for the norm of a vector f in R^{n}.

For example, \left\langle \right f, f\rangle = \left\right\|f\|^{2}

In this case, f dot f without further squaring is equal to \left\right\|f\|^{2}.

But in |<f,g>|^2, you need compute f dot g, and THEN you still square its absolute value.

Is that correct?