How do we interpret the determinant intuitively? Well, here is one way!

This video was requested by Thecalculatorman on reddit!

A few quick notes:

* There are limitations to this way of thinking about the determinant, but for the most part it's solid for 3 and 2D objects.

* Finding the area of the transformed unit cube is the same as finding the area of the parallelpiped, just a little easier to explain. In hindsight, I should have added this definition too.

* There is a lot I skipped over, like how to perform the determinant. That wasn't the point of this video. I wanted to give people an intuitive feel for what the determinant was doing underneath.

As always, the simulations were done live on:

https://www.twitch.tv/simuleios

https://www.youtube.com/channel/UCFf6Ag4GdpEjnEy8M8MB3fg

Feel free to follow me on Twitter!

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And the music is from Josh Woodward (sped up 1.5 times):

https://www.joshwoodward.com/

Thanks for watching!

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**Channel:**LeiosOS

**Topics:**Knowledge

Giorgos Sartzetakis3 months agowow

Lbertarian Armed Fight4 months agomy friend im in serach of this Q -> Is time the determinant of all events in the enviroment?

Lee Yuan Zhi4 months ago3 blue 1 brown does a great job as well, highly recommend watching his videos on determinants

Chil4 months agoA lot of people don’t understand Mathematics because of lack of explanation like this!

1.21 Jiggawatts4 months agoI was trapped in the matrix once but used a determinant to get out. True story.

sanchith jain4 months agoI love ur videos

G Sho5 months agoTruly a genius !

Tharindu Kavinda5 months agovery helpful video for matrix

Adwait Shinde6 months agoI love Mathemagics !!

Narender Goud6 months agoAfter so many years, i finally understand. Thank you very much

Anastasiia Havriushenko7 months agoThank you very much for your detailed explanation and the channel in general!

jhonatan riascos7 months ago@maurevelo

azad khan8 months agoI'm not understand anything

netllcn8 months agoA perfect toturial, a terrible background music. Instructer, a good lecture does not need music, because mathematics itself is a beauty.

José Tobias8 months agoJESUS CHRIST.

HOW CAN I THANK YOU ENOUGH?

WHERE DO I SIGN?

Bolor Erdene Bayarmagnai8 months agoI wish I had this video back in school days

tanuj98028 months agoThey never taught this in class.

Ike Exeter8 months agoWhere’s Neo in this.0

Paras Srivastav8 months agoWell if you would simply put it one sentence instead of making a video -> *It's the volume enclosed inside a parallelepiped whose 3 sides are 3 vectors formed by 3 rows of the matrix.* Now the real question is why determinant is always associated with a square matrix?

Pushkar Mahale8 months agoHere we are told to mug up that product of eigen values is the determinant of a square matrix. Thanks for telling why as well.

magnanil1238 months agoWhat 4 years of engineering couldn't teach ... you did it in 2.51 minutes ❤

Mr V8 months agoHow about losing the annoying background music...?

alex Lo8 months agoI wonder when Gauss had work in matrix. Did he have this geometric description in mind?

Sa B8 months agoThis video is really great! Thank you :D

Matan Kribus8 months agoyea but what is that thing you did in the start of the video? im leanring linear algebra

ice breaker8 months agoamazing

Pumpkin8 months agoWhat can a determinant of a 4x4 dimension represent?

Jorge Mercent9 months agoWhat happens when you apply a Matrix Transformation whose det=0 to a unit cube? What will be the resultant cube look like? Is it that there will be infinite possible resultant cubes with infinite shapes?

Suyash Sharma9 months agoThe first question that pops in mind is - Aligning the unit cube along the eigenvectors..... wait...what? How do we even know that the eigenvectors are all perpendicular to each other??? Doesn't it completely depend on the physical transformation being applied as to what 3 vectors will turn out to be eigenvectors???? Like stretching a plastic cube that transforms to a new shape... To be able to apply this type of restricted transformation, you should explcitly mention that - we are applying a restriction on the transformation now to match the volume of a regular transformation (with rotation involved) on the same cube.

Hope you understand my point. Bill Smyth has already clarified it the the matrix is symmetric "so that the eigenvectors are all already orthogonal" but if i'm asked to stretch a Cube A and then take a Cube B and transform it, strictly following the orthogonality, such that the end volume is same as the Stretched Cube A's volume, ofcourse the product of eigenvalues will

Armando Duette9 months agoAl menos haberlo subtitulado al español si el título está en español ☹️

Praapthi Praapthi9 months agowhy our maths teachers does'nt know this.

ANKIT PAL9 months agoCan't get it , what are you guys doing in the beginning , are you are multiplying matrix with cube?

Sourav Mukherjee9 months agoI learnt much more in these three minutes than the entire semester class of linear algebra. It was really awesome and it gave me the feeling that I can see things instead of just solving mechanically

Jimi Khan9 months agoAmazing...

Ruolin Jia9 months agoThe person who found determinant must be a ridiculously intelligent guy.

feridun abi9 months agobut why

vijendhar bhupathi9 months agoHow transformation is made

Lv 69 Mafia Boss [MAXM]10 months agoWow good video. Watching this to get the same love I have for Calculus into Linear Algebra.

Reinaldo Maciel10 months agoPerfect explanation. Incredibly that several teachers takes more than one class to explain it (or try to) .

Patrick HotelEchoRomeo10 months agoDidn't know before that Eigenvector and Eigenvalue have their names from the German language. We call them Eigenvektor and Eigenwert. "Eigen" means something like "its own", "Vektor" means vector and "Wert" means value.

Fredde10 months agoits very fun and easy to prove this with a 2x2 matrix and two vectors u and v that will undergo a transformation. Just calculate absolute value of det(u,v) to find the old area, then calculate the new area: absolute value of det(T(u),T(v)). Then you will easily see after some algebra steps that this new area is equal to absolute value of det(A)*old area

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Shama K10 months agoAmazing video!! I never ever imagined determinants and eigenvectors this way... Thank you so much 👌👌

avinash chowdary10 months agowhy do we want to transform a cube?

Barzhikev Il10 months agoThis is so beautiful I wanna cry

matsu sumo10 months agoIs it useful only if it is Affine transformation??

alex Marshall10 months agowho was Eigen..he/she pops up regular..ie Eigentones

Srikanth kola10 months agoHow to form cube with matrix

Not understood

Pladimir Vutin10 months agoI was never taught this when we learned about determinants. We were only taught how to find one, not what it actually was.

Xav Nimportnawak10 months agoThank you for that video.

I've red in a book that first, the determinant was found in the pattern of solution for equations systems. You shift the equation system with a matrix*(x,y,z) vector, apply the solutions pattern, and you have a determinant... I don't remember well... would make a video about that?