Exterior algebra on Banach Space Commutative Diagram
作者
Mike Battaglia
最近上传
11 年前
许可
Other (as stated in the work)
摘要
Commutative diagram showing exterior algebra on Banach Space. Based on this commutative diagram example by Stefan Kottwitz.
Commutative diagram showing exterior algebra on Banach Space. Based on this commutative diagram example by Stefan Kottwitz.
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% Commutative diagram with edges passing under/over
% Jan 7, 2009, Stefan Kottwitz
% http://texblog.net
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
%%%<
\usepackage{verbatim}
\usepackage[active,tightpage]{preview}
\usepackage{subfig}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{5pt}%
%%%>
\begin{comment}
:Title: Commutative diagram with crossing edges
:Tags: Matrices; Diagrams
:Author: Stefan Kottwitz
:Slug: commutative-diagram
\end{comment}
\begin{document}
\begin{tikzpicture}
\matrix (m) [matrix of math nodes, row sep=3em,
column sep=3em]{
& \|\cdot\| & & \|\cdot\|^* \\
\Lambda(\|\cdot\|) & & \Lambda(\|\cdot\|)^* & \\
& \|\cdot\|/S & & (\|\cdot\|/S)^* \\
\Lambda(\|\cdot\|/S) & & \Lambda(\|\cdot\|/S)^* & \\};
\path[-stealth]
(m-1-2) edge node [fill=white] {dual} (m-1-4)
edge node [fill=white] {exterior} (m-2-1)
edge [densely dotted] node [pos=0.75,fill=white] {quotient}(m-3-2)
(m-1-4) edge node [fill=white] {subspace} (m-3-4)
edge node [fill=white] {exterior} (m-2-3)
(m-2-1) edge [-,line width=6pt,draw=white] (m-2-3)
edge node [pos=0.75,fill=white] {dual} (m-2-3)
edge node [fill=white] {quotient} (m-4-1)
(m-3-2) edge [densely dotted] node [pos=0.75,fill=white] {dual} (m-3-4)
edge [densely dotted] node [fill=white] {exterior} (m-4-1)
(m-4-1) edge node [fill=white] {dual} (m-4-3)
(m-3-4) edge node [fill=white] {exterior} (m-4-3)
(m-2-3) edge [-,line width=6pt,draw=white] (m-4-3)
edge node [pos=0.75,fill=white] {subspace} (m-4-3);
\end{tikzpicture}
\end{document}