Conjugate Symmetry

linear-algebra

Definition

Conjugate Symmetry

A map $⟨\cdot ,\cdot ⟩:V\times V\to \mathbb{C}$ on a complex vector space $V$ is conjugate-symmetric if

$$⟨u,v⟩=\overline{⟨v,u⟩}\forall u,v\in V.$$

Setting $u=v$ gives $⟨v,v⟩=\overline{⟨v,v⟩}$, so $⟨v,v⟩\in \mathbb{R}$.