User Tools

Site Tools


Plugin installed incorrectly. Rename plugin directory '_include' to 'include'.
Plugin installed incorrectly. Rename plugin directory '__include' to 'include'.
lecture_19

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
lecture_19 [2017/05/06 10:05] rupertlecture_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*}   - 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 we obtain the **orthogonal projection formula**:+{{anchor:proj}}So we obtain the **orthogonal projection formula**:
 \[ \pp=\ppp=\frac{\vv\cdot\ww}{\|\ww\|^2}\ww.\] \[ \pp=\ppp=\frac{\vv\cdot\ww}{\|\ww\|^2}\ww.\]
  
lecture_19.txt · Last modified: by rupert

Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki