5 ms·
Matrices, diagrammatically
- marxshrugged 11y agoI am still trying to wrap my head around this, but the parallels with functional programming are striking.
- Garlef 11y agoString 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/
- kzrdude 11y agoThis reminds me of something I never understood fully: Penrose's tensor notation.
- mrcactu5 11y agoI 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.
- JadeNB 11y agoBaez 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_linear_systems.html https://golem.ph.utexas.edu/category/2015/05/props_for_linea... .
- lisper 11y agoBest to start at the beginning and read through: http://graphicallinearalgebra.net http://graphicallinearalgebra.net
- Garlef 11y agoVery 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