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authorAdrian Kummerlaender2017-03-19 19:03:02 +0100
committerAdrian Kummerlaender2017-03-19 19:03:02 +0100
commit88527c8758aeb33bd4f43cc5f2103d4a2a518020 (patch)
treec4b4b0e0d1e137d060fc8ac1a18b02a411dce786
parentc28538f7850775ff3c08d6a1b522a7a3f8eda5cb (diff)
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Fix spacing in linear algebra digest
-rw-r--r--content/lineare_algebra.tex3
1 files changed, 2 insertions, 1 deletions
diff --git a/content/lineare_algebra.tex b/content/lineare_algebra.tex
index a92a3a8..2269ca9 100644
--- a/content/lineare_algebra.tex
+++ b/content/lineare_algebra.tex
@@ -547,7 +547,7 @@ Seien $\K \in \{\R, \mathbb{C}\}$ und $V$ ein $K$-Vektorraum mit Skalarprodukt,
Sei $V$ endl. dim. VRaum mit SKP, $\phi \in End(V)$ und $B$ ONB, dann:
-\vspace*{-5mm}
+\vspace*{-6mm}
\begin{align*}
\phi \text{ ist Isometrie } &\Leftrightarrow \phi(B) \text{ ist ONB von } V \\
&\Leftrightarrow D_{BB}(\phi) \text{ orthogonal / unitär}
@@ -559,6 +559,7 @@ Sei $A \in U(n)$, dann gibt es $S \in U(n)$, sodass $S^{-1} A S$ Diagonalmatrix.
Sei $A \in O(n)$, $d_+ := dim(Eig(A,1))$, $d_- := dim(Eig(A, -1))$ und $l = \frac{1}{2}(n - d_+ - d_-)$, dann existiert $S \in O(n)$, sodass $S^{-1} A S$ die folgende Blockgestalt hat:
+\vspace{-4mm}
$$\begin{pmatrix}
I_{d_+} & 0 & \hdots & \hdots & 0 \\
0 & -I_{d_i} & \ddots & \ddots & \vdots \\