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Functions are vectors! This perspective lets us apply the tools of linear algebra to computational problems from image and geometry processing to machine learning and light transport—and provides a natural explanation for Fourier series. Let's explore:

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Max Slater

2,933 subscribers

30,457 görüntüleme • 3 yıl önce •via X (Twitter)

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chandler profil fotoğrafı
chandler3 yıl önce

@rohansawhney1 wow nice, your blog/site helped motivate to get back to tech writing and I wrote about the same topic!!

Max Slater profil fotoğrafı
Max Slater3 yıl önce

@rohansawhney1 Cool post!

Platypussy in Bio profil fotoğrafı
Platypussy in Bio3 yıl önce

@algekalipso Aren't you technically using the tools of functional analysis? 😅

Gustavo Leite 🦀 profil fotoğrafı
Gustavo Leite 🦀3 yıl önce

Hey Max! What do you use to create your figures? I'm particularly interested in how you plotted the surfaces in the autodiff article from last year.

Max Slater profil fotoğrafı
Max Slater3 yıl önce

Almost all static figures are made in - the surfaces are actually traced over plots from a 3D graphing app. I wouldn't really recommend it though, it's a lot of manual work. The interactive figures use d3.js / three.js.

Gustavo Leite 🦀 profil fotoğrafı
Gustavo Leite 🦀3 yıl önce

Thanks a lot!

Tomas Skrivan profil fotoğrafı
Tomas Skrivan3 yıl önce

I was thinking about this some time ago. The rendering equation (4.18) in Veach's thesis can be interpreted as Jacobi iterative method. What about using something more advanced like conjugate gradient? Unfortunately, I was never able to turn it into something useful.

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🧵1/n This thread covers the linear algebra for modern computer graphics, bridging geometry, physics, and computation. Video 1: Vector Spaces & Cartesian Coordinates Source: CMU. 👇Video 2: Vector Operations, Vector Spaces, Functions as Vectors, and Vectors in Coordinates
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🧵1/n This thread covers the linear algebra for modern computer graphics, bridging geometry, physics, and computation. Video 1: Vector Spaces & Cartesian Coordinates Source: CMU. 👇Video 2: Vector Operations, Vector Spaces, Functions as Vectors, and Vectors in Coordinates

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the first free interactive linear algebra textbook: - vectors and matrices - dot product and vector product - determinants - matrix ranks - eigenvalues and eigenvectors
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I genuinely thought “linear algebra” meant stuff like 2x = y. Then you open the class and suddenly you’re multiplying giant boxes of numbers. The whole subject gets way easier to understand once you see the core idea: a matrix can act like a rule, a vector can describe a location, and the rule can move that location. That’s why linear algebra shows up everywhere from computer graphics to engineering to machine learning. #LearnOnTikTokContest
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I've been obsessed with motion amplified videos lately. By utilizing high definition video & image processing, the tiniest of movements are amplified into clearly seen real-time motion. Clips from RDI Technologies & RMS Ltd. dynamically demonstrate what these systems are capable of. Potential problems become highlighted, with the software able to overlay force vectors & provide analysis, and also filter for specific frequencies to view resonance. The invisible, visible. I need to try this out for myself...

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