Vectors and Matrices in Trace Diagrams

Snippets Page

How matrices operate when inserted into trace diagrams… includes lots of examples.

# Source Code

$$ABC \leftrightarrow \tikz[heighttwo]{\draw(0,0)to(0,2)node[small matrix,ellipse,pos=.5]{ABC};} =\tikz[heighttwo]{\draw(0,0)to(0,2) node[small matrix,pos=.25]{C}node[small matrix,pos=.5]{B}node[small matrix,pos=.75]{A};} \quad\text{and}\quad \bfv^T A\bfw \leftrightarrow \tikz[heightoneonehalf]{ \draw(0,0)node[vector]{\bfw}to[with small matrix={A}](0,1.5)node[vector]{\bfv};},$$


## Basic Vectors

%vector
$\tikz{\draw(0,.2)node[vector]{$v$}to(0,.8);}$
%covector
$\tikz{\draw(0,.2)to(0,.8)node[vector]{$v$};}$


## Matrix Coefficients

The matrix coefficients or elements:

    $$a_{ij}=\bse^i A\bse_j \leftrightarrow \tikz[heightoneonehalf]{\draw(0,0)node[vector]{i}to[with small matrix={A}](0,1.5)node[vector]{j};}.$$


## Trivalent Diagrams

\tikz[trivalent,heighttwo]{
\draw(0,0)node[small vector]{${\sf n}_{n-l}$}
to node[small matrix]{$\mathbf{X}$}node[pos=.75,rightlabel]{$n$}(0,2)node[small vector]{${\sf n}_{n-k}$};}


## Trace, Determinant, Pfaffian, and Other Invariants

See this snippet.

page revision: 8, last edited: 15 Feb 2010 15:40