There are a lot of proof about Cauchy-Schwarz inequality, there is also an entire book on it.
This is a proof without many advantages with respect to others, rather being very mechanic, however it is the only way someone reached my blog
Cauchy-Schwarz inequality states that:
Let’ s see that this inequality comes shortly from axioms of a vector space and from definition of scalar product
and inequality follows.
The quality of this proof is that it comes out from the axioms of a vector space, unfortunately it does not bring an intuitive insight about this fundamental tool for analysis.
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