From 6dec7fde10d67e649cd7e8c2dc00e61f47a4503a Mon Sep 17 00:00:00 2001
From: Adrian Kummerlaender
Date: Thu, 8 Sep 2016 21:23:09 +0200
Subject: Add calculation info to section on orthogonal projections

---
 lineare_algebra.tex | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

(limited to 'lineare_algebra.tex')

diff --git a/lineare_algebra.tex b/lineare_algebra.tex
index 71c6f31..8bcbd48 100644
--- a/lineare_algebra.tex
+++ b/lineare_algebra.tex
@@ -425,9 +425,10 @@ Entsprechend gilt: $V = U \oplus U^\perp$
 
 \subsubsection*{Orthogonale Projektionen}
 
-\begin{description}[leftmargin=!,labelwidth=15mm]
-	\item[Definition] $\pi_U : V \rightarrow U, u + u^\perp \mapsto u$
-	\item[Abstand]    $d(v, U) = ||u^\perp|| = ||\pi_{U^\perp}(v)||$
+\begin{description}[leftmargin=!,labelwidth=20mm]
+	\item[Definition] $\Pi_U : V \rightarrow U, u + u^\perp \mapsto u$
+	\item[Bestimmung] $\Pi_U(a) = \sum_{i=1}^n \langle a,u_i \rangle u_i$
+	\item[Abstand]    $d(a, U) = ||u^\perp|| = ||a - \Pi_U(a)||$
 \end{description}
 
 \subsection*{Affine Teilräume}
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