# Cauchy Schwarz inequality on scalar terms

The following equations are derived from Quantum information theory, which requires the use of Cauchy Schwarz inequality for a proof.

I am quite puzzled by the second term in the summation, which consists of a sum over the product of a square norm and an absolute value i.e. the product of two scalars!, my question is : isn't cauchy schwarz inequality strictly applied to vectors only?

I found the closest thing to the one i had is the Rn dimension from Wiki, but xi, yi there are component of a vector in which my case isn't.

• – Tom Collinge Mar 27 '16 at 12:56
• Do you mean it is true that n = 1 i.e. scalar? still works? – el psy Congroo Mar 27 '16 at 12:59
• If $n = 1$ then all it says is $(xy)^2 \le x^2y^2$ and since they are the same this is clearly true. – Tom Collinge Mar 27 '16 at 13:02