TITLE: How can I learn about doing linear algebra with trace diagrams?
QUESTION [11 upvotes]: There is a wikipedia article.  There is a paper by Elisha Peterson.  I tried reading these but they don't seem to click for me.
Are there books or other resources for learning how to do linear algebra with trace diagrams?

REPLY [12 votes]: to Greg Kuperberg: Use of such diagrams probably starts in mid 19th century (Sect. 4.9 A BRIEF HISTORY OF BIRDTRACKS). If you find "spiders" or “birdtracks” too silly, I vote for the somewhat unwinged "tensor diagrams." 

So why give these diagrams a new name, and not call them “Feynman diagrams” or "tensor diagrams"? I needed a distinct name to distinguish them from the more traditional uses of diagrams. The difference is that here diagrams are not a mnemonic device, an aid in writing down a Feynman integral that is to be evaluated by other techniques. I did not call them "tensor diagrams" as that is too close to “invariant tensor operators”, the Wigner-Eckart theorem, and the 3n-j diagrams that are only a prelude to a computation. Here “birdtracks” are everything, all calculations are carried out in terms of birdtracks, from start to finish.