TITLE: A user's guide to Penrose graphical notation?
QUESTION [21 upvotes]: Penrose graphical notation seems to be a convenient way to do calculations involving tensors/ multilinear functions. However the wiki page does not actually tell us how to use the notation.
The several references, especially ones with Penrose as author, must be good places to start. But it is now the summer holiday and I am away from my school library. So I am wondering whether someone here has a nice introduction to "the use" of Penrose graphical notation.
Thanks!

REPLY [2 votes]: TensorNetwork.org is a great place to see introductory examples, while Hand-waving and interpretive dance: an introductory course on tensor networks is a great reference to understand this notation more systematically. Additionally, here are some examples I made to introduce people to Penrose graphical notation:




My first image is inspired by the math3ma blog on tensor network diagrams.