Complex Inner Product Space

linear-algebra

Definition

Complex Inner Product Space

A complex inner product space is a complex vector space $V$ equipped with an inner product

$$⟨\cdot ,\cdot ⟩:V\times V\to \mathbb{C}$$

that is sesquilinear, conjugate-symmetric, and positive definite.

Example: ${\mathbb{C}}^n$ with $⟨x,y⟩={\sum }_{i=1}^n{x}_i\overline{y_i}$.