String Diagrams for Linear Algebra
graphicallinearalgebra.net
String Diagrams for Linear Algebra
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Re: String Diagrams for Linear Algebra
#2Matrices, although great for computers, are often complicated and unintuitive. This blog was my first insight into an alternative symbolic interpretation for Linear Algebra. It has often led to problems and complicated equations being represented with far more simplicity. As well as teaching me to be more flexible and creative with my own notations.
Re: String Diagrams for Linear Algebra
#3This is poor man's Chu spaces http://chu.stanford.edu
Re: String Diagrams for Linear Algebra
#4Matrices, although great for computers, are often complicated and unintuitive. This blog was my first insight into an alternative symbolic interpretation for Linear Algebra. It has often led to problems and complicated equations being represented with far more simplicity. As well as teaching me to be more flexible and creative with my own notations.
Agreed. The graphical notation elegantly demonstrates that a lot of symbolic manipulation just boils down to pushing parts of a formula around until they fit a specific pattern, so that you can apply an identity and replace it with a different pattern.
Re: String Diagrams for Linear Algebra
#5We have established that there is a homomorphism called θ from B, the PROP of diagrams, to Mat, the PROP of matrices.
I've never seen such a complex subject as linear algebra presented with such clarity and simplicity.
Re: String Diagrams for Linear Algebra
#6Is this (closely) related to Penrose tensor notation https://en.wikipedia.org/wiki/Penrose_graphical_notation?
Re: String Diagrams for Linear Algebra
#7We have established that there is a homomorphism called θ from B, the PROP of diagrams, to Mat, the PROP of matrices. I've never seen such a complex subject as linear algebra presented with such clarity and simplicity.
Are you being sarcastic?
Re: String Diagrams for Linear Algebra
#8Without an ad blocker, this page redirects to a malware landing page for me.
Re: String Diagrams for Linear Algebra
#9Is this (closely) related to Penrose tensor notation https://en.wikipedia.org/wiki/Penrose_graphical_notation ?
Yes
Re: String Diagrams for Linear Algebra
#10Is this (closely) related to Penrose tensor notation https://en.wikipedia.org/wiki/Penrose_graphical_notation ?
Yes. The difference is that here the operation represented by putting wires next to each other is the direct sum, whereas in the Penrose notation the operation is the tensor product. They're both examples of the string diagram notation for monoidal categories. (https://forum.azimuthproject.org/discussion/2335/lecture-73-...)