Definition. Let $V$ be a vector space over $\mathbb{R}$ (or $\mathbb{C}$). A map $b\colon V \times V \to \mathbb{R}$ is a symmetric bilinear form, if $ b(v,w)=b(w,v) \quad \forall v,w \in V $ $ b(\alpha_1 v_1 + \alpha_2 v_2,w) = … Continue reading Lecture 12