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-rw-r--r--lineare_algebra.tex7
1 files changed, 4 insertions, 3 deletions
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}