- #1
divB
- 87
- 0
Hi,
I want to show:
[tex]
\|f-jg\|^2 = \|f\|^2 - 2 \Im\{<f,g>\} + \|g\|^2
[/tex]
However, as far as I understand, for complex functions [itex]<f,g> = \int f g^* dt[/itex], right? Therefore:
[tex]
\|f-jg\|^2 = <f-jg, f-jg> = \int (f-jg)(f-jg)^* dt = \int (f-jg)(f+jg) dt = \int f^2 + jfg - jfg + g^2 dt = \|f\|^2 + \|g\|^2
[/tex]
Where is my wrong assumption?
Thanks.
I want to show:
[tex]
\|f-jg\|^2 = \|f\|^2 - 2 \Im\{<f,g>\} + \|g\|^2
[/tex]
However, as far as I understand, for complex functions [itex]<f,g> = \int f g^* dt[/itex], right? Therefore:
[tex]
\|f-jg\|^2 = <f-jg, f-jg> = \int (f-jg)(f-jg)^* dt = \int (f-jg)(f+jg) dt = \int f^2 + jfg - jfg + g^2 dt = \|f\|^2 + \|g\|^2
[/tex]
Where is my wrong assumption?
Thanks.