I'm learning about Support Vector Machines and would like to recap on some basic linear algebra. More specifically, I'm trying to prove the following, which I'm pretty sure is true:(adsbygoogle = window.adsbygoogle || []).push({});

Let ##v1## and ##v2## be two vectors in an inner product space over ##\mathbb{C}##.

Suppose that ## \langle v1 , v2 \rangle = ||v1|| \cdot ||v2|| ##, i.e. the special case of Cauchy Schwarz when it is an equality. Then prove that ##v1## is a scalar multiple of ##v2##, assuming neither vector is ##0##.

I've tried using the triangle inequality and some other random stuff to no avail. I believe there's some algebra trick involved, could someone help me out? I really want to prove this and get on with my machine learning.

Thanks!

BiP

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

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

# Cauchy Schwarz equality implies parallel

Loading...

Similar Threads - Cauchy Schwarz equality | Date |
---|---|

I Validity of proof of Cauchy-Schwarz inequality | Nov 23, 2016 |

A Question on Cauchy-Schwarz inequality | Oct 3, 2016 |

Cauchy-Schwarz inequality | Jul 11, 2011 |

Cauchy, Schwarz, Bunyakovsky | Feb 24, 2011 |

Cauchy-Bunyakovsky-Schwarz inequality | Oct 9, 2008 |

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