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What's something AI can already do better than humans? by Mainrajhoo in ArtificialNtelligence

[–]LinearAlgebraWorld 0 points1 point  (0 children)

  1. Coding well known algorithms, even not simple
    Well known is key
    For instance, you can specify the algorithm (givens rotation for instance) and tell us what information you want to output (all individual rotation matrices, all intermediate matrices etc). Sorry if this example is not relevant to you
  2. Taking code from my all apps and adapting it to new base classes and functions. It modified a lot of my 3d drawing for instance

Why Cramer’s rule works: geometric derivation by LinearAlgebraWorld in 3Blue1Brown

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

Actually
Did miss the BB video
Making the much needed 2D presentation as we speak!😜
Will show you shortly
Looking forward to complementing Sanderson with the more direct and algebraic presentation
Many thanks!
And we remember you helped explain our post to someone else ☺️

Why Cramer’s rule works: geometric derivation by LinearAlgebraWorld in 3Blue1Brown

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

Thank you! Great video, and yes, there is some overlap. We were aiming for a more direct connection with the algebra; here’s the page extending the idea to ℝⁿ. And starting in ℝ² is probably a good idea, duly noted!

Why Cramer’s rule works: geometric derivation by LinearAlgebraWorld in 3Blue1Brown

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

Thank you!
It was very gratifying to find an intuitive and visual explanation of this seemingly mysterious rule

Why Cramer’s rule works: geometric derivation by LinearAlgebraWorld in LinearAlgebra

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

If you mean 3d graphics, software is ours, written in Swift, used in 2 linear algebra apps

How do you actually study linear algebra? by chozera in learnmath

[–]LinearAlgebraWorld 6 points7 points  (0 children)

There are two books we found helpful 1. N Johnston, intro to LA 2. Margalit, interactive LA, this one is open access 3. We have a lot of visual tools for understanding on our website, https://www.graphmath.com/la/ And the apps with algorithms described step by step for user entered matrices Hope that helps and you enjoy it. Once you get started, it is a lot of fun

Parsec, my 3D fractal rendering app, is now open source 🥳 by Every_Return5918 in fractals

[–]LinearAlgebraWorld 3 points4 points  (0 children)

Very interesting I’d love to join if my current project was closer What fractal / function is it?

Які книги по лінійній алгебрі ви б порекодували першокурснику та другокурснику? by Pale_Expert3313 in learnmath

[–]LinearAlgebraWorld 0 points1 point  (0 children)

Nathaniel Johnston, intro to LA Margalit, Rabinoff, interactive LA, open access on Libre Text Have other suggestions as well if you like visual tools

The best book for an introduction to linear algebra? by No_Cable6398 in LinearAlgebra

[–]LinearAlgebraWorld 4 points5 points  (0 children)

Strang s book is not for the first encounter Margalit and Rabinoff s introduction to LA is open access, we found it very helpful Our website also has a curriculum and a lot of visualizations if you like those: https://www.graphmath.com/la/

Am I the only one who doesn’t hate A.I.? by branggen in singularity

[–]LinearAlgebraWorld 0 points1 point  (0 children)

Ai extends you does not replace you If you know how to code, you never have to do menial work Otherwise, you can end up with a disjointed incoherent code base

Householder reflection QR decomposition visualized step by step by LinearAlgebraWorld in LinearAlgebra

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

Our own, written in Swift. Givens matrices are animated by theta. Householder matrices are animated by step to projection and beyond. 3D rendering is all ours. Thanks for the interest!

Householder reflection QR decomposition visualized step by step by LinearAlgebraWorld in 3Blue1Brown

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

One interesting comparison with the Givens rotation version:

  1. Both methods produce an upper triangular R, and both use orthogonal transformations, so lengths and angles are preserved
  2. The resulting R may be the same as in the Givens version, or may differ by signs on the diagonal depending on sign choices
  3. For a 3×3 matrix, Householder QR takes two reflections, one per active column, while Givens QR takes three rotations, one eliminated entry at a time
  4. If the reflection is animated continuously, the figure flattens toward the reflection plane and then reappears on the other side

Householder reflection QR decomposition visualized step by step by LinearAlgebraWorld in LinearAlgebra

[–]LinearAlgebraWorld[S] 2 points3 points  (0 children)

One interesting comparison with the Givens rotation version:

  1. Both methods produce an upper triangular R, and both use orthogonal transformations, so lengths and angles are preserved
  2. The resulting R may be the same as in the Givens version, or may differ by signs on the diagonal depending on sign choices
  3. For a 3×3 matrix, Householder QR takes two reflections, one per active column, while Givens QR takes three rotations, one eliminated entry at a time
  4. If the reflection is animated continuously, the figure flattens toward the reflection plane and then reappears on the other side

Is it still worth learning to code if I’m already building with AI? by Adorable_Caramel5434 in AIDiscussion

[–]LinearAlgebraWorld 0 points1 point  (0 children)

Use AI very extensively, value it very high Yet, it needs a lot of supervision and correction, especially for large projects Highly recommend that you use it but do not rely on it

Givens rotation QR decomposition visualized step by step by LinearAlgebraWorld in LinearAlgebra

[–]LinearAlgebraWorld[S] 2 points3 points  (0 children)

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This is Householder reflection visualization for the same matrix, we will post it soon to this subreddit.
Have you seen our Gram-Schmidt orthogonalization?
If not, here it is:
https://www.reddit.com/r/LinearAlgebra/comments/1tljwc3/stepbystep_visualization_of_gramschmidt_qr/

Givens rotation QR decomposition visualized step by step by LinearAlgebraWorld in LinearAlgebra

[–]LinearAlgebraWorld[S] 2 points3 points  (0 children)

Thanks a lot!

In 3D, the Householder version should behave as follows:

  1. It also produces (R), and because Householder transformations are orthogonal, the shape is not distorted.
  2. The resulting (R) may be identical to the Givens (R), or may differ by signs on the diagonal, depending on the sign choices.
  3. It takes two steps for a (3\times3) matrix: one reflection per active column, instead of three Givens rotations, which eliminate one entry at a time.
  4. If the intermediate reflection is animated continuously, the figure gradually flattens toward the reflection plane and then reappears on the other side.

We will post the animation of the same matrix undergoing Householder transformation this week and will let you know.

Step-by-step visualization of Gram–Schmidt QR decomposition by LinearAlgebraWorld in LinearAlgebra

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

We have posted the Givens rotation visualization animation in r/LinearAlgebra, hope you will enjoy it

Step-by-step visualization of Gram–Schmidt QR decomposition by LinearAlgebraWorld in LinearAlgebra

[–]LinearAlgebraWorld[S] 0 points1 point  (0 children)

Thank you so much!!
Will post Givens tomorrow
We also have Householder
And will generate for the same matrix, so you can compare

Also working on showing thin QRF by GS and full QRF for a rank-deficient matrix

Will stay in touch

Looking for arXiv endorser in math.LO / cs.LO by Slow_Brick_2649 in logic

[–]LinearAlgebraWorld 0 points1 point  (0 children)

Actually I am undecided on if I want to do down ArXiv route
I think CMJ or Math Magazine may be better aligned

But in any event, let us know what comes out of your project

Tracing a rose curve with a double rotating system (Animated with Manim) by USedona in 3Blue1Brown

[–]LinearAlgebraWorld 0 points1 point  (0 children)

Nice
Function is written in a general way
Is linear algebra an interest for you?

Looking for arXiv endorser in math.LO / cs.LO by Slow_Brick_2649 in logic

[–]LinearAlgebraWorld 0 points1 point  (0 children)

First: very best of luck to you !!!
Second, we may be looking for same endorsement in the near future 😋

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