Earlier quoted context omitted.
Everyone's seen/knows them already
Well, even if "everyone" knows it, at some point you have to come across it for the first time. https://xkcd.com/1053/
Everyone's seen that XKCD already.
A Programmer’s Intuition for Matrix Multiplication
51–60 of 95 posts
Re: A Programmer’s Intuition for Matrix Multiplication
#52I've always found the bipartite graph conceptualization of matrix multiplication the most intuitive, and especially so if you're familiar with neural networks: https://www.math3ma.com/blog/matrices-probability-graphs
That is genuinely a really fun way to look at it, thank you for linking this! Especially this fits nicely with Markov matrices where you have N input nodes and N output nodes and the sum of all of the probabilities coming out of one of the nodes needs to equal 1. What I might find a little more difficult to teach to people through this lens is the phenomenon of eigenvectors, but I suppose that's to be expected—nothin…
>What I might find a little more difficult to teach to people through this lens is the phenomenon of eigenvectors
Why? Eigenvectors are simply inputs to the network where the output keeps its shape, that is, at most it gets rescaled, as if you had applied a uniform gain to the components, but otherwise it will be the same as the input.
Re: A Programmer’s Intuition for Matrix Multiplication
#53This comes up occasionally. I don't find it to be particularly helpful, even though I do think betterexplained has been a strong source of gaining intuition into various subjects. Recognizing though that method of understanding something is pretty personal, I will say that what really helped me refresh was the 3Blue1Brown Essence of Linear Algebra series on Youtube. If you're trying to better grasp the subject, do yo…
Everyone's seen/knows them already
I haven't. I'm glad notsuoh posted the link.
Re: A Programmer’s Intuition for Matrix Multiplication
#54Matrices are a fun way to stretch the mind. They are easy to grasp yet very dissimilar to numbers. Sometimes they can be used to represent numbers and we can use our matrix intuition to answer questions about regular numbers. You can define functions on matrices just like you define them on numbers. Multiplication is a function. The determinant is a function. You can even take derivatives of these functions. The deri…
Don't forget the matrix exponential which might certainly blow the mind of a lot of people here. Matrices as exponent - who would have thought that possible! https://en.wikipedia.org/wiki/Matrix_exponential
det(e^A) = e^(tr(A))
Pure magic.
Re: A Programmer’s Intuition for Matrix Multiplication
#55[deleted]
Re: A Programmer’s Intuition for Matrix Multiplication
#56What is some good intuition around matrix inverses?
Re: A Programmer’s Intuition for Matrix Multiplication
#57I've always found the bipartite graph conceptualization of matrix multiplication the most intuitive, and especially so if you're familiar with neural networks: https://www.math3ma.com/blog/matrices-probability-graphs
That is genuinely a really fun way to look at it, thank you for linking this! Especially this fits nicely with Markov matrices where you have N input nodes and N output nodes and the sum of all of the probabilities coming out of one of the nodes needs to equal 1. What I might find a little more difficult to teach to people through this lens is the phenomenon of eigenvectors, but I suppose that's to be expected—nothin…
An eigenvector would correspond to the "stationary distribution" of the Markov transition matrix represented by the graph. (think "page rank")
Re: A Programmer’s Intuition for Matrix Multiplication
#58This comes up occasionally. I don't find it to be particularly helpful, even though I do think betterexplained has been a strong source of gaining intuition into various subjects. Recognizing though that method of understanding something is pretty personal, I will say that what really helped me refresh was the 3Blue1Brown Essence of Linear Algebra series on Youtube. If you're trying to better grasp the subject, do yo…
3Blue1Brown is really great for learning/refreshing math. He has great visualizations.
I especially enjoyed this video (not exactly a math tutorial more of a cool explanation): https://www.youtube.com/watch?v=OkmNXy7er84
Re: A Programmer’s Intuition for Matrix Multiplication
#59If we're talking about 3D rendering then a matrix multiplication with a vector are just projections: A 3x3 matrix that transforms a vector is nothing else than that vector being projected onto the 3 axis which are inside the 3x3 matrix. This is very easy to see visually. A matrix times matrix multiplication (eg 3x3 times 3x3) is just projecting the axis of one matrix onto the other: expressing the coordinate system i…
> I always hated the dull mathematic definition of "a matrix represents a linear map" because what the matrix actually represents is completely context dependent.
The projection and translation matrices you mentioned represent restricted sets of linear maps in some vector space, but the meaning of the restriction is also captured in other mathematical structures. See affine spaces and projective spaces.
Re: A Programmer’s Intuition for Matrix Multiplication
#60Earlier quoted context omitted.
Well, even if "everyone" knows it, at some point you have to come across it for the first time. https://xkcd.com/1053/
Everyone's seen that XKCD already.