Q: Prove that if y and z are linear functionals (on the same vector space) such that [x,y]=0 whenever [x,z]=0, then there exists a scalar ξ such that y=ξz.(adsbygoogle = window.adsbygoogle || []).push({});

(Hint: if [x_{0},z]≠0, write ξ=[x_{0},y]/[x_{0},z].)

I'm fairly certain there's an obvious proof using the dual basis, but this is in the section before that, so I'm trying to do it without that, and can't seemed to get the proper result. Any help would be great, 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!

# Question on a proof.

Loading...

Similar Threads - Question proof | Date |
---|---|

I Proof of Existence of Tensor Product ... Further Question .. | Mar 17, 2016 |

Proof question: the sum of the reciprocals of the primes diverges | Jun 13, 2014 |

Question on a proof by induction | Sep 30, 2012 |

Question in Proof of second order condition with linear constraints | Jun 21, 2011 |

Orthogonality theorem proof method question | May 9, 2011 |

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