Very good presentation. My one nitpick is at 4:58, where you should probably specify that we could pick either orientation of vectors to have positive area: we simply have to pick SOME orientation to be positive, and pick counterclockwise by convention.

@brokemathstudent

3 ай бұрын

Yep, it should be pointed out that it’s precisely a consequence of Rule 1 that certain orientations are considered positive and others are negative - namely, if we decided that A(j, i) = 1 in Rule 1 instead, then A(i, j) would be -1 and all the areas will be negative of what they normally are.

@mathematicalmachinery7934

3 ай бұрын

lol it took me a few minutes paused to figure out where the “orientation” came from before I saw rule 1

@mellowInventor

3 ай бұрын

​@@brokemathstudentnegative is just the opposite of whatever the reference orientation is. It gets more difficult to calculate at A^N dimensions!

@pauldirc..

2 ай бұрын

What is defination of area and why it is a into b in case of rectangle

@adityamrai3892

2 ай бұрын

wonderful presentation! How do you make these animations? Is this Manim?

5 days ago I typed into the KZread search bar " Why are determinants like that?" but I couldn't find an intuitive enough explanation -- you read my mind and I'm excited to watch this video!

@Mr0rris0

2 ай бұрын

You are now a determinator 😎

@macchiato_1881

2 ай бұрын

​@@Mr0rris0im convinced most mathematicians have a horrible sense of humor because of this comment.

@Mr0rris0

2 ай бұрын

@@macchiato_1881 well I ain no mathitician if that helps

@osamaqidwai7800

4 күн бұрын

You didnt find 3b1b's video on this topic??

So humble of you to shoutout the small mathematicians like Leibniz.

@sunnythebridger7529

3 ай бұрын

😢Yep, leibniz is so underrated.

@jimpim6454

3 ай бұрын

small? are you joking?

@natan6218

3 ай бұрын

​@@jimpim6454 yes, they are

@antonioplaza8557

3 ай бұрын

"small" ?

@0MVR_0

3 ай бұрын

@@jimpim6454 intended as a joke as shoutouts are given to high profiles of lesser prestigue as a free hand up

11:16 "we dont have enough colors" yes thus appears the biggest problem for going into higher dimensions

@mitchratka3661

3 ай бұрын

Bro the irony of you representing the problem of a lack of representations in another form is so funny lmao

@TheArtOfBeingANerd

3 ай бұрын

Imagining a world where we only have two colors and hence can't imagine the three dimensions we live in

I have a PhD in mathematics (granted not algebra) and the 10th minute (plus some wine) caused the increasingly rare epiphany as to the n! terms in the determinate formula. Thank you, sir.

@fazemega1222

2 ай бұрын

I have a PhD as well, no I have let me check ... yes umm of course my kidergarten diploma here (totally the same as a PhD ;) right?) of course it is about the study of "Super Proportional Vector Fields with a distinct continuus Z Functions ". It's the real deal guys, real deal ...you know that pesky... riemman million dollar problem, the answer is right there. I found out that it stops at 10^363262363 + 2353534532^2. Totally did not invent my field of study and the solution right now. Of course not. Why should I do that. In all seriousness, congrats on having a PhD the only thing I have to brag is that I like math???. I know it is really out of place in a youtube channel called "broke math student" but still.

I am facinated by the fact that you call unit vectors i-hat, j-hat and k-hat, while I am being taught about them as i-cap, j-cap and k-cap. There can be languages inside languages sometimes.

@guntera3845

3 ай бұрын

I‘ve only ever heard the i-hat version. Good to know the i-cap version but I think it is more exotic.

@whannabi

3 ай бұрын

People saying "cap" are the cool kids.

@mgsquared5204

3 ай бұрын

Are you from the US? I’ve never heard i-cap in my life. Cap feels like such a British word. 😂

@guidomista8448

3 ай бұрын

That's how I was taught too. Î ĵ ƙ are all hats.

@saketsreevallabhrambhogaraju

3 ай бұрын

@@mgsquared5204 Naa, i'm not from US, I'm from India.

This is the first time I’ve seen a decent visualization of where determinants come from without using the words “geometric algebra” talking about how it’s so much better than vector algebra! Also, I had no idea that the whole “crossing” thing was part of the standard! I thought that was just a weird tangent for talking about multivector rearrangement, I hadn’t figured out how to relate that back to vector algebra. Genius explanation!

Leibniz really needed that shoutout, it's always good to see big creators help smaller ones. (great video)

5:54 This part made me realize the connection between the cross product and the determinant

12:07 > _"how many swaps required? use braid diagrams"_ niice

I finally understood what the determinant is. Thank you for making this video

I had seen the permutation formula for the determinant years ago and had always wondered what on earth it had to do with an area. This was a great explanation!

Okay this channel is VERY good. I appreciate math videos more when they help me understand how to discover my formulas. Also, you do a good job pausing in your speech to give me time to process what I saw. This is something I hope to see more mathtubers do well, but you've killed it

@dgaul123

3 ай бұрын

Yeah he had perfect pace, not too fast and not too slow.

In Geometry I I learnt the definition of the determinant with the permutations, and it was really odd, as it just poped up, without further explanation. This video's topic should have been that class XD

amazing video !! i loved your coverage of the topic, and your way of breaking apart and explaining the subject was very well done and easy to follow !! i cant wait to see more stuff from you :)

@persik7gd

3 ай бұрын

AZALI!? Love your music!

What a great presentation vectors are such a rich area

This video catch my attention so hard that I actually stopped studying just to watch this beauty explanation and visual representation of the Determinant of the Matrix

I can already see your channel crossing 1M if this level of content is maintained. Cheers mate. 👏👏

Hands down best video on determinant. Further I have yet to see this so clearly laid out in any text book.

If only KZread had an option to like the video's description. Your references saved me. Also, I love your logical and understandable approaches to show the properties of determinants. Thank you!

Thank you a lot for this video, I have been asking that same question for the last 5 years and yet could not find anything but the simple geometric demostration or the derivation for the simple 2d determinant. Most of people stop there, but for me it feels like proof by induction, it works but you dont learn anything. After watching the video I feel like the awnser was always there! and that I was overcomplicating things, as always the genius of linear algebra is in its simplicity, you made it pretty simple every step of the way!

Brilliant video, it's the first time I deeply understand why the determinant is a volume and also a really elegant derivation of Leibniz formula !

Most intuitive presentation of the determinant i have seen!

On the braid crossings, in exterior/geometric algebra one can represent the volume elements by means of the wedge product, and then the crossing numbers can come from NOR operations applied in switching said wedges.

this is so cool, u know what are the general questions in the mind of a math student, thanks a lot for making this video

you're amazing dude, never seen math that way, you blew my mind, keep going with your videos, cheers from Brazil

Oh my god, I loved this. Illustrating the geometric object associated to each algebraic step during dimensions two and three was fantastic, and then the inclusion of braid groups!

Excellent Video! I really like proving all the complex applications, by first starting with simple rules. I think, this is the best way to teach mathematics in schools too. Please try to do more video like this whenever you can, as it will be a big service for humanity.

im taking linear algebra right now, this video explained in the terms and notation the professor used!! I LOVED THIS TYYSM

This video is a real treasure, it is one of the best and most important videos/lessons regarding the topic of linear algebra! Thank you so much! 😊

Incredible! Even though this channel is still small, it's amazing!

6 years using matrix and vectors, and now I have came up why we do multiply that parameter by this and so on. Cool video!!

Sheer brilliance! All math videos should be this good. 🎉😊

this is one of the most awesome videos on determinants

Congratulations! This a fascinating, amene, as well as relaxing, approach to a usually non well explained algebraic geometry. I love this kind of videos. Thanks for the post. +1 subscriber❤

Such a good video, helped a lot with understanding/recalling what i've studied a year ago :D I was particularly confused with why determinant is defined by permutaions, thank you for your effort!

A comment for the algoirthm. I have no words on how great of a video this is, hope more are on the way!

More than a genius. I had never been taught in this way. WOW physical interpretation is awesome

hloo sir ,love from india , u explained the topic which even 3b1b failed me to, this shows ur understanding of concept. furthermore i want u to keep making videos on this linear algebra topic its just seems to out of the box to understand this

This is a really excellent explanation for one of the more arcane formulas from my linear algebra course.

please keep making educational math content, this is magical

I deeply enjoyed watching this brief explanation

Simply amazing, always wanted to see/do this! Thanks

I've been looking for a video on this topic for months, thanks

Fantastic explanation. One thing that you didn't address but I personally always found important, is that in 2 dimensions if you swap the coordinates and flip the sign of one, you get a normal vector: same size but orthogonal to the original. The determinant is the dot product of this one orthogonal vector, and the other original one. Carthesian dot products are independent of the choice of coordinate systems, and thus, are a physical value. That value is the (signed) area.

This was excellent, the determinant always annoyed me but this is so illustrative and makes me want to learn about symmetric groups more. Thank you so much for such a good video!!

bro this is EXACTLY what I'm trying so hard to read and understand in my textbook rigght now... your explanation is perfectly clear and blowing my mind, kind of :0 thanks for this although I will saay, my book is also throwing differentials at us so to me it still feels just more complex and yet also beautiful :D

Thank you for your precious time.

That is an very interesting visualization of determinant . It has benefited me a lot

thank you so much, this Is such a great video, i understood more the determinant thanks to you!

I have done my highschool (cal.maths or add maths) and I never knew determinants can be visualized this way and that it was this simple!!

I've been looking for video like this for a loooooooong time...

This is one of the best (if not THE best) video I've seen on the topic! Also, regarding 8:55 - I really hope you're not an Austrian planning on moving to Germany... 😛

Also, it's useful to note that a circular permutation of an even sequence (ab, abcd, ....) has alternating sign, given by mod 2 formula, while an odd sequence (a, abc, abcde, ...) has unchanging sign. That's rather useful to rearrange subsequences of symbols in an order more fitting for partitions sorting, that also doesn't affect the total ordering.

Oh this is amazing. I'm taking a group theory course, without having taken linear algebra, and i get somewhat lost when they talk about matrix groups. Having recently learned about alternating groups (groups of even permutations), it was really cool to see them crop up in determinants

Best outro in a math video ever.

Great video, thank you! The best explanation of where matrices come from that I've ever seen! The only request is to make the time when the final exercises are shown on the screen to be longer than one second and move them to the center. When I stop the video at the last second, I can't read the bottom lines because they're covered with KZread video buttons.

Great work ❤! You're killing it 💪

thank you for this great explanation

Beautiful presentation.

This is a fantastic explanation!

Amazing animation with great explanations. Thanks! Btw, did you use Manim for animations?

masterpiece explanation video.

Beautiful bro, keep up with good work 💪💪

this is the best video of mathematics taht i saw

As someone going into their first year of a mathematics degree THANK YOU SO MUCH!!!!!!!

absolutely amazing video

Best explaination!

Not sure if this was mentioned, but orientation of spaces is intrinsic to geometric algebra. Love this demonstration! Thank you.

Best outro for a math video

Thank you for this video 🙏🏻❤️

Wonderful explanation!! Thank you so much! :-)

Great video. Keep it up!

In a few hours i have an Algebra exam, and this video was quite helpful, if one exercise is determinant based, i will update :)

@martinjimenez821

3 ай бұрын

I passed 😃. Sadly, there was no determinant based exercise, great video tho

I love the content, how did u do this amazing video,what video-rappresentation tools did u use?

Man, this is soo cool seeing your videos. Can you share the source code for the scenes?

I'm right now just studying differential forms and multilinear functions, I guess this video will be really good to it

Amazing video ❤

The ending XD Love it!!!!!!!!!

fantastic video.

Simply amazing

Amazing visuals

YES YES YES, you showed the method of calculation too, oh god I feel like the determinant has been a little neglected as a concept to be explained. If you're searching for such concepts, how about the hessian matrix and its determinant. After all it's pretty important for multivar calculus

Nice job!

Stand proud. You can cook.

The First Time Someone Explained To me The DETERMINANT :-o

I had to slow the video down to see that last frame. Task 4 requires writing a textbook which is uhhh. Anyway amazing video, i loved your manim animations ❤

It's also interesting to point out, that determinant in 2d is a bivector, in 3d it's a trivector and etc. In other words it's a pseudoscalar.

Very nice!

You rock Thanks for this elimination

Seeing your videos you seems like a very interesting and smart person , I saw your last video on doing maths alone and when in the last part the quote by Robert pyar from Zen in motorcycle on pursuing highest knowledge highly resonated with me can you give me more recommendation on such books and quotes

beautiful!!!

oh how i wish these videos existed on youtube 10 years ago

holaaa , podris decirme de que libro sacaste ese desarollo algebraico??? gracias espero tu respuesta

"Some of the most interesting mathematics happens when we see where 'nonsense' leads us" . Dang what a bar. Definitely stealing this one.🤣

amazing video

Fantastic ❤

That was just continuing to apply definitions... thx.

what softwre are you using for demonstrating such matrix and vector graphics.

This is very good, time to make the broke math student rich