(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex]\beta[/tex] be a basis for a finite dimensional inner-product space.

b) Prove that is < x, z > = < y, z> for all z [tex]\in[/tex] [tex]\beta[/tex], then x = y

2. Relevant equations

3. The attempt at a solution

start with the Cauchy-Schwarz:

|< x, z >| [tex]\leq[/tex] ||x|| ||z||

then because <x,z> = <y,z>

|< y, z >| [tex]\leq[/tex] ||x|| ||z||

so y = x, is this correct?

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# Homework Help: Inner Product Spaces

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