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!

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# Question on a proof.

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