Complex Dot Product

The complex dot product, also known as the Hermitian dot product, is an inner product that uses the complex conjugate.

Definition §

Complex Dot Product

Let $\vec{u},\vec{v}\in {\mathbb{C}}^n$ be two vectors in the complex vector space. Then, the complex dot product is defined as:

$$\vec{u}\cdot \vec{v}=u_1{\bar{v}}_1+u_2{\bar{v}}_2+\cdots +u_n{\bar{v}}_n$$