Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# L2 norm of complex functions?

Loading...

Similar Threads - norm complex functions | Date |
---|---|

I Norm of a Linear Transformation ... Another question ... | Mar 3, 2018 |

I Norm of a Linear Transformation ... Junghenn Propn 9.2.3 ... | Mar 2, 2018 |

I Differentiation on R^n ...need/ use of norms ... | Mar 1, 2018 |

I R^n as a normed space ... D&K Lemma 1.1.7 ... | Feb 28, 2018 |

Norm of a Complex Number | Jan 26, 2013 |

**Physics Forums - The Fusion of Science and Community**