## A simple proof of Cauchy-Schwarz inequality

### September 18, 2007

[reader be aware: this is a post for getting attention from the web, you may get these information elsewhere and probably also better written]

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 blogðŸ™‚

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.