Difference between r1.2 and the current
@@ -8,4 +8,15 @@
WpEn:Pythagorean_theorem
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벡터의 피타고라스 정리
Thm 1.2.11 (Theorem of Pythagoras)
If $\bf u$ and $\bf v$ are orthogonal vectors in $R^n,$ then $\left\| \bf u + \bf v \right\|^2 = \left\| \bf u \right\|^2 + \left\| \bf v \right\|^2 $
Proof
$\left\| {\bf u} + {\bf v} \right\|^2$
$= ({\bf u}+{\bf v}) \cdot ({\bf u}+{\bf v})$
$= \left\| {\bf u} \right\|^2 + 2({\bf u}\cdot{\bf v}) + \left\| {\bf v} \right\|^2$
$= \left\| {\bf u} \right\|^2 + \left\| {\bf v} \right\|^2$
(Anton/Busby Contemporary Linear Algebra)
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Up: [[정리,theorem]]
벡터의 피타고라스 정리
Thm 1.2.11 (Theorem of Pythagoras)
If $\displaystyle \bf u$ and $\displaystyle \bf v$ are orthogonal vectors in $\displaystyle R^n,$ then $\displaystyle \left\| \bf u + \bf v \right\|^2 = \left\| \bf u \right\|^2 + \left\| \bf v \right\|^2 $
Proof
Thm 1.2.11 (Theorem of Pythagoras)
If $\displaystyle \bf u$ and $\displaystyle \bf v$ are orthogonal vectors in $\displaystyle R^n,$ then $\displaystyle \left\| \bf u + \bf v \right\|^2 = \left\| \bf u \right\|^2 + \left\| \bf v \right\|^2 $
Proof
$\displaystyle \left\| {\bf u} + {\bf v} \right\|^2$
$\displaystyle = ({\bf u}+{\bf v}) \cdot ({\bf u}+{\bf v})$
$\displaystyle = \left\| {\bf u} \right\|^2 + 2({\bf u}\cdot{\bf v}) + \left\| {\bf v} \right\|^2$
$\displaystyle = \left\| {\bf u} \right\|^2 + \left\| {\bf v} \right\|^2$
(Anton/Busby Contemporary Linear Algebra)$\displaystyle = ({\bf u}+{\bf v}) \cdot ({\bf u}+{\bf v})$
$\displaystyle = \left\| {\bf u} \right\|^2 + 2({\bf u}\cdot{\bf v}) + \left\| {\bf v} \right\|^2$
$\displaystyle = \left\| {\bf u} \right\|^2 + \left\| {\bf v} \right\|^2$
Up: 정리,theorem