Відео

The scaling factor being a higher dimensional shear operation seems so obvious in retrospect. Thank you so much for the animation!

So cool! It's definitely going to be helpful for me

awesome job!

Great video! One off the best I've seen on the topic!

so everyone knows, nowdays is common to hear that matrices do transformations, which is misleading what is actually happening is that in algebra, there is a concept called linear transformations that are just equations with some constraints this equations end up as a system of equations with each equation having a series of products between constants and variables, such as: a*x + b*y = k c*x + d*y = h and all linear transformations have a matrix representation, which, in this case, is: | a b | | x | | k | | c d | * | y | = | h | so the matrix abcd represents a specific linear transformation over some coordinates xy this transformation can be whatever you want, but if you want specific properties for this transformations, you can specify it in the original equations, figure them out and then the matrix comes in free

excellent explanations

It is possible to visualize 4D geometry, and even to show it graphically and animate it.

when a student tries to become a teacher. thats you and this video. NICE

excellent

Thank you!

any translation in low dimensions can be represented as a transformation in higher dimensions (n+1). Great illustration !

this is exactly what i wanted!!

Really nice

Great video

Great explanation, thanks a lot!!!

Wow😲. So helpful to me. Thanks a lot.

Now make a 4D game using 5D matrices (5x5 matrices)

It's actually possible to extend complex numbers to handle 3D rotations and translations. The 3D analog of the complex numbers are well known as the quaternions, but there also exist the dual-quaternions which are capable of describing any proper rigid transformation, ie rotation and translation. There's also an interesting way to extend these to higher dimensions as well as other types of transformations. While the components grow faster than matrices, doubling with each additional underlying dimension rather than going to the next square, they provide much smoother interpolation. I actually noticed a few times in this video where an object appeared to shrink as it was moving before ending up at the same size as it started.

Very cool. Now, it is just a small step to quaternions😀. By the way, since there was a short blender clip inside the video, I just wanted to mention that I'm working on a library that realizes much of the manim tools inside blender. If you are interested, let me know.

great video! at 6:32 please use 'dots' instead of 'x' for matrix multiplication :)

Great video! I didn't knew homogeneous coordinates intuitively. ! Nice visuals

Linear algebra is still a very new concept for me but this video was very nifty! Awesome work :)

Great graphics and explanation. I thought I was watching a 3 Blue 1Brown video at times. Well done!

Super cool video, really helpful to build intuition.