Matrices and Graph

#1

Post by jgrodziski » Sat, Jul 15, 2023, 8:27 AM UTC

Matrices and Graph
thepalindrome.org

Re: Matrices and Graph

#2

Post by bionhoward » Sat, Jul 15, 2023, 11:41 AM UTC

Beautiful illustrations, thank you for sharing.

Re: Matrices and Graph

#3

Post by duckqlz » Sat, Jul 15, 2023, 11:52 AM UTC

Does anyone know how the graph illustrations were created? I have driven myself mad with tikz and dot .

Re: Matrices and Graph

#4

Post by elliotwagner » Sat, Jul 15, 2023, 11:57 AM UTC

duckqlz wrote: post #3

Does anyone know how the graph illustrations were created? I have driven myself mad with tikz and dot .

I would like to know this too

Re: Matrices and Graph

#5

Post by dustingetz » Sat, Jul 15, 2023, 12:03 PM UTC

what book to read to develop these concepts and intuitions with engineering level of math (not proofs)?

Re: Matrices and Graph

#6

Post by dpflan » Sat, Jul 15, 2023, 12:16 PM UTC

dustingetz wrote: post #5

what book to read to develop these concepts and intuitions with engineering level of math (not proofs)?

I don't know how proof heavy this course is and it is not specialized on graphs: "Computational Science and Engineering I" -- Gilbert Strang (MIT)

https://ocw.mit.edu/courses/18-085-computational-science-and...

Re: Matrices and Graph

#7

Post by zmgsabst » Sat, Jul 15, 2023, 12:29 PM UTC

This is especially fascinating when you consider graphs/diagrams are a way to encode math.

Re: Matrices and Graph

#8

Post by EsportToys » Sat, Jul 15, 2023, 12:31 PM UTC

duckqlz wrote: post #3

Does anyone know how the graph illustrations were created? I have driven myself mad with tikz and dot .

looks like Manim.

Re: Matrices and Graph

#9

Post by EsportToys » Sat, Jul 15, 2023, 12:35 PM UTC

Fun fact: this is only valid for domains that have a notion of "selfness", i.e. that there is such thing as an "identity matrix" for the quantities.

Consider the following square matrix:

            TSLA APPL GOOG MSFT    
    Alice | 100   5     0    1
    Bob   |  0    30   100   5
    Carol |  2    2     2    2
    Dan   |  0    0     0  1000

An input vector of stock prices gives an output vector of net worths. However, that is about the only way you can use this matrix. You cannot transform the table arbitrarily and still have it make sense, such as applying a rotation matrix -- it is nonsensical to speak of a rotation from Tesla-coordinates to Google-coordinates. The input and output vectors lacks tensor transformation symmmetries, so they are not tensors.

This is also why Principal Component Analysis and other data science notions in the same vein are pseudoscience (unless you evaluate the logarithm of the quantities, but nobody seems to recognize the significance of unit dimensions and multiplicative vs additive quantities)

Re: Matrices and Graph

#10

Post by aziis98 » Sat, Jul 15, 2023, 1:03 PM UTC

EsportToys wrote: post #9

Fun fact: this is only valid for domains that have a notion of "selfness", i.e. that there is such thing as an "identity matrix" for the quantities. Consider the following square matrix: TSLA APPL GOOG MSFT Alice | 100 5 0 1 Bob | 0 30 100 5 Carol | 2 2 2 2 Dan | 0 0 0 1000 An input vector of stock prices gives an output vector of net worths. However, that is about the only way you can use this matrix. You cannot tra…

Yeah, this is also the case if the table is not square as the values can't represent edges any more. So its more something like the rows and columns should index the same "thing".

By the way by changing the graph representation we can give meaning even to non square matrices as described in this article https://www.math3ma.com/blog/matrices-probability-graphs