aboutsummaryrefslogtreecommitdiff
diff options
context:
space:
mode:
authorAdrian Kummerlaender2016-09-08 21:23:09 +0200
committerAdrian Kummerlaender2016-09-08 21:23:09 +0200
commit6dec7fde10d67e649cd7e8c2dc00e61f47a4503a (patch)
tree3c870972ac332f9f6a0ab8ddbd6b15a2e26d4638
parent5f46c42899a20fbebce559412a66c6ea0e3f83aa (diff)
downloadmath_reference_sheets-6dec7fde10d67e649cd7e8c2dc00e61f47a4503a.tar
math_reference_sheets-6dec7fde10d67e649cd7e8c2dc00e61f47a4503a.tar.gz
math_reference_sheets-6dec7fde10d67e649cd7e8c2dc00e61f47a4503a.tar.bz2
math_reference_sheets-6dec7fde10d67e649cd7e8c2dc00e61f47a4503a.tar.lz
math_reference_sheets-6dec7fde10d67e649cd7e8c2dc00e61f47a4503a.tar.xz
math_reference_sheets-6dec7fde10d67e649cd7e8c2dc00e61f47a4503a.tar.zst
math_reference_sheets-6dec7fde10d67e649cd7e8c2dc00e61f47a4503a.zip
Add calculation info to section on orthogonal projections
-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}