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| -rw-r--r-- | lineare_algebra.tex | 7 |
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} |