Відео

This makes so much more sense. Basically redefine ijk-hat to be in the direction of your transformed matrix.

Amazing video, thank you! Does Span mean the same as Range?

Good video but the gen Z formatting 🤮🤮🤮🤮

Can we F'ing not generic AI voice with constantly shifting visuals?

mini 3blue1brown

beautiful

This made diagonalization more confusing. thanks chump!

absolutely stunning. deserves to have more views and you more subscribers <3333

Didn't understand a single word of this, but it was pretty!

I am surprised that this has only 15k views

Is it that: if the curve intersects a previous point it had already been at, then it is not one to one?

Sir can you send me example of diagonalisable 5×5 matrix example

Wow! Extremely helpful

Truely Underrated 🌟

Wth you are so underrated

I was thinking the other day what was used before analytical geometry. And then discovered synthetic geometry. I think there's a need for a balance between analytical and synthetic geometry. What do you think? Lovely animation, btw ❤

Guys how i understand we dividing some linear transformation to different steps that easier to calculate, i mean our p matrix help us to change basis and D changes sizes and P inverse ends the work,now i have question: Is it correct to say that P realize some rotation that we need and D just change sizes????

Hi with regards to the PDP^-1. The P^-1 is convert to the new basis after which scale by D and then rotate back to the standard basis by P. Am i correct?

I can watch these in a loop all dal long!

Thank you so much!!!

Superb video!

HOW does this not have more views?? Best visualization of this concept I have ever seen

Wow, this is incredible. I must say you have done a very good job with this video, and you explained the concepts of diagonalization very concisely. Thanks!

wow!

Amazing video 🎉

u are more helpful than my teacher what

Man i bearly even comment on any youtube videos, but i feel i really need to express how i feel about your videos. At first 3Blue1Brown brought me close to mathematics, since then, im obsessed with it. There are many really good YT channels, that introduce interesting topics in this field, but man you're so good. Please keep up the work man, i know you're not as big right now, as you would appreciate it, but if you keep on going, with this style, i bet you will be as big as 3B1B or bigger. Thank you for your educational content!

Remember us when you're big😢😢

Good lord I hate that voice.

Very insightful! Question: when you read the equation at 4:27 you read it from left to right, but aren't the matrices composited from right to left?

how are you sampling your random lines? You say its unlikely that there are zero solutions, but it’s not a 0% chance like there being one solution is.

good stuff

Thank you

Thanks! Great video

Great video , greetings from Spain !

Fun fact: to calculate the largest power of a matrix, where the exponent still fits in 64bit unsigned long, there are only 128 Multiplications needed. Example: You want to calculate 5^14. We split the exponent in binary: 5^(2¹+2²+2³) = 5² × (5²)² × ((5²)²)² = 6.103.515.625 . We only have to x := x², and if the current bit is on, we multiply our result with the current power, then we square x again... So to calculate powers up to about 4 Billion, u only need at most 64 multiplications. 32 for the squaring and at most 32 for the result multiplication. Since computers do not have more difficulties with larger numbers , that reduces the amount of calculations by an insane amount.

there's a great book called Linear and Geometric Algebra by Alan Macdonald. while a good portion of it is about building the foundation of geometric algebra (a very clean way of unifying many parts of linear algebra by defining a new operation on vectors), the best part about the book is that it teaches linear algebra and linear transformations without much matrix usage; there's like one or two chapters covering matrices, as they are important, but most discussion of linear transformations is matrix-free. i really like it because i think matrices are so heavily tied with linear transformations that the two tools can get conflated with one another

Great video and visuals. Thanks!

It s dfficult for me to understand HOW to prove the intercesections of lines in the simplest of cases. Could you give a reference where such a proof can be found?

Nice

Great intuition bro… great teaching too

This shows your very deeply intuition

Very good… can u do some physical basics as well… like Bell local realism Inequalities and double slit exp… i know it’s physics but the way you intuit may help

Great video sir. Thank you so much Sir❤

until the end when i checked the sub and view count, i thought that this was some big math youtuber that i haven't heard of yet. great work man really well made

Is this video inspired by the advent of code exercise? 😅

The video is amazing. Only thing I would complain about is that you didn't write the conclusion theorem in words at the end since I got lost in the pictures

Why so low views? Low subs? Beyond me!!.. May be changing channel name might help?

Any new video soon?

It's beautiful but I think the title should be changed or maybe the content. The title is a bit misleading as it doesn't actually show a function that takes a sphere as an input