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Introducing Operation Matrix Because Matrix operations generally break kids’ brains on whiteboards… Matrices aren't just numbers- they are transformations in space Now can actually SEE the geometry: every addition, multiplication, inverse, eigenvalue, and eigenvector becomes a transformation in real-time space. What it visualizes: • Basic ops (add/subtract/multiply) • Transpose,... show more

shadows

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58,942 просмотров • 7 месяцев назад •via X (Twitter)

Наука и технологии Образование

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Комментарии: 47

Фото профиля shadows

shadows7 месяцев назад

try it here

Фото профиля Pavel Boytchev

Pavel Boytchev7 месяцев назад

I've tried to teach matrices with a game. Here is the matrix carousel where cubes are transformed by matrices and students have to match animations with matrices: Live game: Instructions:

Фото профиля shadows

shadows7 месяцев назад

wow!!! this is so interesting

Фото профиля ekim

ekim7 месяцев назад

@threejs Kids…surrrrreeeee yea I’m gonna use this for my “kid” (bookmarks). 😀

Фото профиля shadows

shadows7 месяцев назад

@threejs 😀😀

Фото профиля Rami

Rami7 месяцев назад

Nice work! I would have loved to have something like ths for studying eigen values for the first time.

Фото профиля shadows

shadows7 месяцев назад

Good luck with it!!

Фото профиля Aaryaman Sharma

Aaryaman Sharma7 месяцев назад

@threejs Awesome!

Фото профиля shadows

shadows7 месяцев назад

thanks!!

Фото профиля Allone

Allone7 месяцев назад

This is brilliant. Matrices clicked for me the moment I stopped thinking of them as numbers and started seeing them as spatial transformations. Making that visual and interactive will save so many students hours of confusion.

Фото профиля shadows

shadows7 месяцев назад

@AllanGuetta hope it can help students :)

Фото профиля Allone

Allone7 месяцев назад

Yeah, spatial learning will now have a strong edge with this current tools

Фото профиля Savith Dasanayaka

Savith Dasanayaka7 месяцев назад

wow. this is amazing.

Фото профиля Enrique Meza Costeno

Enrique Meza Costeno7 месяцев назад

Wow! Great you inspired me.

Фото профиля shadows

shadows7 месяцев назад

nice!! :)

Фото профиля Vladislav Kruteniuk

Vladislav Kruteniuk7 месяцев назад

thats cool

Фото профиля shadows

shadows7 месяцев назад

Thanks

Фото профиля Jacobers_COM

Jacobers_COM7 месяцев назад

I love this! I’ve personally struggled with matrix operations! Mainly visualization of the movement so this is gold! Thank you!!

Фото профиля shadows

shadows7 месяцев назад

glad you liked it :)

Фото профиля Charlie T Beagle

Charlie T Beagle7 месяцев назад

Amazing! Wish I had this 30 years ago.

Фото профиля shadows

shadows7 месяцев назад

i know.. i also wanted something like that during university days :)

Фото профиля L’Écho du Corbeau

L’Écho du Corbeau7 месяцев назад

Very very nice!

Фото профиля shadows

shadows7 месяцев назад

thanks :)

Фото профиля esp

esp7 месяцев назад

very cool

Фото профиля shadows

shadows7 месяцев назад

thanks :)

Фото профиля O💤

O💤7 месяцев назад

Thanks for sharing

Фото профиля shadows

shadows7 месяцев назад

glad you liked it :)

Фото профиля Lamborghini Alfredo

Lamborghini Alfredo7 месяцев назад

This is a good use of vibe coding

Фото профиля Anton Malofeev 💙

Anton Malofeev 💙7 месяцев назад

glowy animation is looks just amazing! watched it several times.. really. feels like it is reward from calculation

Фото профиля shadows

shadows7 месяцев назад

thanks!!! glad you liked it :)

Фото профиля High Jack

High Jack7 месяцев назад

Oh this would've saved me so much pain back in the day. Seeing the geometry makes the math click instantly.

Фото профиля shadows

shadows7 месяцев назад

I know, right! 😀

Фото профиля bee

bee7 месяцев назад

Superb. Please make a 2D visualizer as well. This is helpful for students getting into Tech Art or VFX TD roles as well 🥰

Фото профиля shadows

shadows7 месяцев назад

will work something out.. thanks for the suggestion

Фото профиля If Beli

If Beli7 месяцев назад

Finally someone with geometrical and visual explanation.

Фото профиля Kartikey Pandey

Kartikey Pandey7 месяцев назад

Wow incredible 😲

Фото профиля shadows

shadows7 месяцев назад

Thanks!! Glad you liked it..

Фото профиля Hasan Aboul Hasan

Hasan Aboul Hasan7 месяцев назад

really great! this is what we should be building and helping in education.

Фото профиля shadows

shadows7 месяцев назад

Hope it helps

Фото профиля Robn

Robn7 месяцев назад

Would be interesting to see the affects of iterative factoring algos

Фото профиля shadows

shadows7 месяцев назад

that's some food for thought :)

Фото профиля ∞ 𝕁uan ℂarlos

∞ 𝕁uan ℂarlos7 месяцев назад

Really cool! :)

Фото профиля shadows

shadows7 месяцев назад

thanks!! just hoping will help students enjoy learning Matrix operations :)

Фото профиля Giedrius Trump

Giedrius Trump7 месяцев назад

Beautiful!

Фото профиля Vogel Mann

Vogel Mann7 месяцев назад

bro you call this operation matrix and cant even center the view orbit.

Фото профиля shadows

shadows7 месяцев назад

really

Фото профиля Ascent817

Ascent8177 месяцев назад

would've saved my linear algebra grade

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36,580 просмотров • 4 месяцев назад

$MIT FILMED THE LECTURE WHERE THEIR MOST LEGENDARY LINEAR ALGEBRA PROFESSOR EXPLAINS WHY EVERY GPS SIGNAL EVERY MEDICAL SCAN AND EVERY AI MODEL ON EARTH IS SECRETLY SOLVING A PROBLEM THAT HAS NO SOLUTION This is Gilbert Strang, MIT, 18.06 Linear Algebra, lecture 15. The professor whose textbooks sit in over 3,000 universities across 135 countries and whose course has been watched by millions of engineers and mathematicians worldwide. He opens with one claim - when equations have no solution, you do not give up. You solve the closest problem that can be solved. He starts with a vector b and a line through a. The projection of b onto that line is the point closest to b that actually lives on the line. The key is a right angle. The error - the gap between b and its projection - must be perpendicular to a. That one geometric fact produces the entire formula. The projection is a times a transpose b divided by a transpose a. One fraction. The numerator is a matrix. The denominator is a number. Then the projection matrix. Every projection is carried out by a matrix P that multiplies b and lands on the line. That matrix has two properties that define all projections everywhere. First, P transpose equals P - the matrix is symmetric. Second, P squared equals P - project twice and you stay where you are. The first projection moves you onto the line. The second leaves you there. Then higher dimensions. Instead of projecting onto a line, project onto a plane. Instead of one vector a, you have a matrix A with two columns spanning the plane. The error vector must now be perpendicular to both columns - perpendicular to the entire plane. That condition produces one matrix equation. A transpose times the error equals zero. The error lives in the null space of A transpose, which is exactly perpendicular to the column space of A. The four fundamental subspaces appear without being called. Then the formula for n dimensions. The projection matrix is A times A transpose A inverse times A transpose. Strang warns the room not to simplify it by canceling A inverse against A - A is not square, it has no inverse, and the formula cannot be pulled apart. The only case where it simplifies to the identity is when A spans the whole space and the projection is b itself. Watch the moment he applies the formula to fitting a line through three points that no line can pass through. Three equations, two unknowns, no solution. He writes the matrix, writes the right-hand side, and shows that multiplying both sides by A transpose produces an equation that always has a solution. That equation is the foundation of least squares, GPS triangulation, and every regression model trained in 2026. A data scientist I know rewatched this lecture before building a recommendation system from scratch. Said it was the first time the normal equations felt like geometry rather than a formula someone handed down to memorize. Free on YouTube, MIT OpenCourseWare, filmed over 20 years ago. bookmark this and watch later - after this lecture every unsolvable equation you meet will feel like a projection waiting to be found$

MIT FILMED THE LECTURE WHERE THEIR MOST LEGENDARY LINEAR ALGEBRA PROFESSOR EXPLAINS WHY EVERY GPS SIGNAL EVERY MEDICAL SCAN AND EVERY AI MODEL ON EARTH IS SECRETLY SOLVING A PROBLEM THAT HAS NO SOLUTION This is Gilbert Strang, MIT, 18.06 Linear Algebra, lecture 15. The professor whose textbooks sit in over 3,000 universities across 135 countries and whose course has been watched by millions of engineers and mathematicians worldwide. He opens with one claim - when equations have no solution, you do not give up. You solve the closest problem that can be solved. He starts with a vector b and a line through a. The projection of b onto that line is the point closest to b that actually lives on the line. The key is a right angle. The error - the gap between b and its projection - must be perpendicular to a. That one geometric fact produces the entire formula. The projection is a times a transpose b divided by a transpose a. One fraction. The numerator is a matrix. The denominator is a number. Then the projection matrix. Every projection is carried out by a matrix P that multiplies b and lands on the line. That matrix has two properties that define all projections everywhere. First, P transpose equals P - the matrix is symmetric. Second, P squared equals P - project twice and you stay where you are. The first projection moves you onto the line. The second leaves you there. Then higher dimensions. Instead of projecting onto a line, project onto a plane. Instead of one vector a, you have a matrix A with two columns spanning the plane. The error vector must now be perpendicular to both columns - perpendicular to the entire plane. That condition produces one matrix equation. A transpose times the error equals zero. The error lives in the null space of A transpose, which is exactly perpendicular to the column space of A. The four fundamental subspaces appear without being called. Then the formula for n dimensions. The projection matrix is A times A transpose A inverse times A transpose. Strang warns the room not to simplify it by canceling A inverse against A - A is not square, it has no inverse, and the formula cannot be pulled apart. The only case where it simplifies to the identity is when A spans the whole space and the projection is b itself. Watch the moment he applies the formula to fitting a line through three points that no line can pass through. Three equations, two unknowns, no solution. He writes the matrix, writes the right-hand side, and shows that multiplying both sides by A transpose produces an equation that always has a solution. That equation is the foundation of least squares, GPS triangulation, and every regression model trained in 2026. A data scientist I know rewatched this lecture before building a recommendation system from scratch. Said it was the first time the normal equations felt like geometry rather than a formula someone handed down to memorize. Free on YouTube, MIT OpenCourseWare, filmed over 20 years ago. bookmark this and watch later - after this lecture every unsolvable equation you meet will feel like a projection waiting to be found

Lupen

24,677 просмотров • 3 месяцев назад