Stat/Junk
Inner products and Norms
Inner products Definition Defiition 1 (Inner product). A function $\langle \cdot , \cdot \rangle$ : $\mathbb{R}^n \times \mathbb{R}^n → \mathbb{R}$ is an inner product if $\langle x , x \rangle \geq 0$, $\langle x , x \rangle = 0 \Leftrightarrow x = 0$ (positivity) $\langle x , y \rangle = \langle y , x \rangle$ (symmetry) $\langle x + y , z \rangle = \langle x , z \rangle + \langle y , z \rangl..
