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Make Loss on Title Page bigger

This commit is contained in:
Anton Mosich 2022-06-09 16:15:44 +02:00
parent 4b255ca0a3
commit 1592ce8ba3
Signed by: Flugschwein
GPG Key ID: 9303E1C32E3A14A0
1 changed files with 12 additions and 11 deletions
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LinAlg2.tex
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@ -12,7 +12,7 @@
\usepackage{cancel}
\usepackage[ngerman]{babel}
\usepackage{harpoon}
\usetikzlibrary{tikzmark,calc,arrows,angles,math,decorations.markings}
\usetikzlibrary{tikzmark,calc,arrows,arrows.meta,angles,math,decorations.markings}
\usepackage{pgfplots}
\usepackage{framed}
\usepackage[hyperref,amsmath,amsthm,thmmarks,thref,framed]{ntheorem}
@ -87,10 +87,11 @@
\tikzset{%
-||-/.style={decoration={markings,
mark=at position 0.5 with {\draw[thin, -] (-.2,-.2) -- (0, .2);\draw[thin, -] (0, -.2) -- (.2, .2);}},
mark=at position 0.5 with {\draw[thick, -] (-.2,-.2) -- (0, .2);\draw[thick, -] (0, -.2) -- (.2, .2);}},
postaction={decorate}},
}
\begin{titlepage}
\begin{tikzpicture}[remember picture, overlay]
% Trans pride flag
@ -102,18 +103,18 @@ postaction={decorate}},
minimum height=\paperheight] at ([xshift=(\i - 1)*(\paperwidth / 5)]current page.south west) {};
% The Loss
% Panel 1
\draw[very thick, <-] ([xshift = 85pt, yshift = -60pt]current page.north west) -- +(0, -.35\paperheight);
\draw[line width=.5mm, {Stealth[scale=1.3]}-] ([xshift = 85pt, yshift = -60pt]current page.north west) -- +(0, -.35\paperheight);
% Panel 2
\draw[very thick, <-, -||-] ([xshift = -85pt, yshift = -.1\paperheight - 60pt] current page.north east) --
\draw[line width=.5mm, {Stealth[scale=1.3]}-, -||-] ([xshift = -85pt, yshift = -.1\paperheight - 60pt] current page.north east) --
+(0, -.25\paperheight);
\draw[very thick, <-, -||-] ([xshift = -185pt, yshift = -60pt]current page.north east) --
\draw[line width=.5mm, {Stealth[scale=1.3]}-, -||-] ([xshift = -185pt, yshift = -60pt]current page.north east) --
+(0, -.35\paperheight);
% Panel 3
\draw[very thick, ->, -||-] ([xshift = 40pt, yshift = 60pt] current page.south west) -- +(0, .35\paperheight);
\draw[very thick, ->, -||-] ([xshift = 175pt, yshift = 60pt] current page.south west) -- +(0, .35\paperheight);
\draw[line width=.5mm, -{Stealth[scale=1.3]}, -||-] ([xshift = 40pt, yshift = 60pt] current page.south west) -- +(0, .35\paperheight);
\draw[line width=.5mm, -{Stealth[scale=1.3]}, -||-] ([xshift = 175pt, yshift = 60pt] current page.south west) -- +(0, .35\paperheight);
% Panel 4
\draw[very thick, ->] ([xshift = -175pt, yshift = 60pt] current page.south east) -- +(0, .35\paperheight);
\draw[very thick, <-] ([yshift = 120pt, xshift = -25pt] current page.south east) -- +(-.38\paperwidth,0);
\draw[line width=.5mm, -{Stealth[scale=1.3]}] ([xshift = -175pt, yshift = 60pt] current page.south east) -- +(0, .35\paperheight);
\draw[line width=.5mm, {Stealth[scale=1.3]}-] ([yshift = 120pt, xshift = -25pt] current page.south east) -- +(-.38\paperwidth,0);
\draw[very thick] ([xshift = -175+40pt, yshift = 120]current page.south east)
arc [radius=40pt, start angle=0, end angle=90];
% Title, Author & Date
@ -3783,7 +3784,7 @@ $\sigma$ heißt Polarform von $\rho$
\section[Die Singulärwertzerlegung und die Pseudoinverse]{Die Singulärwertzerlegung und die \\Pseudoinverse}
Wir wollen nun für zwei euklidische Vektorräume $V, W$ eine geeignete Normalform bezüglich Orthonormalbasen
Wir wollen nun für zwei euklidische Vektorräume $V, W$ eine geeignete Normalform \\ bezüglich Orthonormalbasen
herleiten. Polarzerlegung besagt für $\alpha \in \Hom(V, V)$, dass Orthonormalbasen $B, B'$ von $V$ existieren
mit
\[
@ -3814,7 +3815,7 @@ Das heißt $\alpha$ lässt sich aus orthogonalen Endomorphismen und Skalierung z
\end{satz}
\begin{proof}
\begin{itemize}
\item $A^* A \in \K^{\nxn}$ selbstadjungiert und positiv semi-definit.
\item $A^* A \in \K^{\nxn}$ selbstadjungiert und positiv semi-definit. \\
Eigenwerte $\lambda_1, \dots, \lambda_n \in [0, \infty)$, ONB $b_1, \dots, b_n$ aus Eigenvektoren.
Sei $\lambda_1, \dots, \lambda_r \in (0, \infty), \lambda_{r+1} = \dots = \lambda_n = 0$
$s_i := \sqrt{\lambda_i}, i\in [n]$