Complex Scalar Product

Description:

• Scalar Product
  • we have standard scalar when $x,y\in {\mathbb{R}}^n$
• For two complex-valued n-vectors, define Hermitian scalar as $x^{H}y:={\sum }_{i=1}^{n}x(i).\bar{y}(i)$
  • $\bar{y}$ is the Complex Conjugate
• The result is the complex number
• The function $||x|{|}_2:=\sqrt{x^{H}x}$ is a norm

$4x^{H}y=||x+y|{|}_2^2-||x-y|{|}_2^2$