Matrices, diagrammatically
graphicallinearalgebra.net
Matrices, diagrammatically
1–8 of 8 posts
Re: Matrices, diagrammatically
#2I am still trying to wrap my head around this, but the parallels with functional programming are striking.
Re: Matrices, diagrammatically
#3This reminds me of something I never understood fully: Penrose's tensor notation.
Re: Matrices, diagrammatically
#4I 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
Yes! That's where I have seen these diagrams before. They are Hopf algebras, which appear both in Electrical Engineering and Theoretical Physics.
Re: Matrices, diagrammatically
#5Best to start at the beginning and read through:
Re: Matrices, diagrammatically
#6I 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 Yes! That's where I have seen these diagrams before. They are Hopf algebras, which appear both in Electrical Engineering and Theoretical Physics.
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... .
Re: Matrices, diagrammatically
#7Very impressive if the author developed this by himself.
But this is a well known idea from category theory:
Re: Matrices, diagrammatically
#8I am still trying to wrap my head around this, but the parallels with functional programming are striking.
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.
This gives rise to these diagrams: