Pole-Polar Relationship b is non-degenerate symmetic bilinear form (e.g.scalar product on $\mathbb{R}^n$) orthogonal complement of a vector subspace $U\subseteq V$ \[U^{\perp}= \left\lbrace v\in V\mid b\left(u,v\right) = 0,\forall u\in U\right\rbrace \] $dimU^{\perp} + dim U = dim V$, but $U^{\perp} \oplus … Continue reading Lecture 15