

Matrices, diagrammatically - graphlinalg
http://graphicallinearalgebra.net/2015/06/09/matrices-diagrammatically/

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lisper
Best to start at the beginning and read through:

[http://graphicallinearalgebra.net](http://graphicallinearalgebra.net)

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mrcactu5
I am guessing these diagrams are taken from Electrical Engineering and not
Quantum Physics.

The blog looks like an expansion of their paper
[http://arxiv.org/abs/1403.7048v3](http://arxiv.org/abs/1403.7048v3)

Yes! That's where I have seen these diagrams before. They are Hopf algebras,
which appear both in Electrical Engineering and Theoretical Physics.

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JadeNB
Baez discussed the paper on the n-Category Café, and it may be easier for the
inexperienced (like me!) to get started there:
[https://golem.ph.utexas.edu/category/2015/05/props_for_linea...](https://golem.ph.utexas.edu/category/2015/05/props_for_linear_systems.html)
.

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Garlef
Very impressive if the author developed this by himself. But this is a well
known idea from category theory:

[http://en.wikipedia.org/wiki/String_diagram](http://en.wikipedia.org/wiki/String_diagram)

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kzrdude
This reminds me of something I never understood fully: Penrose's tensor
notation.

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marxshrugged
I am still trying to wrap my head around this, but the parallels with
functional programming are striking.

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Garlef
String diagrams are a way to describe morphisms (think functions) in monoidal
categories.

A construction using monoidal categories (or a slight generalisation) can be
used to give a categorical model for arrows.

[http://bentnib.org/arrows.pdf](http://bentnib.org/arrows.pdf)

This gives rise to these diagrams:

[https://www.haskell.org/arrows/](https://www.haskell.org/arrows/)

