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--- lecture_19 [2017/04/11 10:39] – [Theorem] rupert
+++ lecture_19 [2017/05/06 10:14] (current) – rupert
@@ Line 14: / Line 14: @@
   - Since $\nn=\vv-\pp$ is orthogonal to $\ww$, we have $\nn\cdot \ww=0$. Hence \begin{align*}&&(\vv-\pp)\cdot \ww&=0\\&\implies& \vv\cdot\ww-\pp\cdot\ww&=0\\&\implies& \pp\cdot\ww&=\vv\cdot\ww\\&\implies& c\ww\cdot \ww&=\vv\cdot\ww\\&\implies& c\|\ww\|^2&=\vv\cdot\ww\\&\implies& c&=\frac{\vv\cdot\ww}{\|\ww\|^2}.\end{align*}
-So
+{{anchor:proj}}So we obtain the **orthogonal projection formula**:
 \[ \pp=\ppp=\frac{\vv\cdot\ww}{\|\ww\|^2}\ww.\]