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 Sartzetakis6 months agowow

Lbertarian Armed Fight7 months agomy friend im in serach of this Q -> Is time the determinant of all events in the enviroment?

Lee Yuan Zhi7 months ago3 blue 1 brown does a great job as well, highly recommend watching his videos on determinants

Chil7 months agoA lot of people don’t understand Mathematics because of lack of explanation like this!

1.21 Jiggawatts7 months agoI was trapped in the matrix once but used a determinant to get out. True story.

sanchith jain7 months agoI love ur videos

G Sho8 months agoTruly a genius !

Tharindu Kavinda8 months agovery helpful video for matrix

Adwait Shinde9 months agoI love Mathemagics !!

Narender Goud9 months agoAfter so many years, i finally understand. Thank you very much

Anastasiia Havriushenko10 months agoThank you very much for your detailed explanation and the channel in general!

jhonatan riascos10 months ago@maurevelo

azad khan11 months agoI'm not understand anything

netllcn11 months agoA perfect toturial, a terrible background music. Instructer, a good lecture does not need music, because mathematics itself is a beauty.

José Tobias11 months agoJESUS CHRIST.

HOW CAN I THANK YOU ENOUGH?

WHERE DO I SIGN?

Bolor Erdene Bayarmagnai11 months agoI wish I had this video back in school days

tanuj980211 months agoThey never taught this in class.

Ike Exeter11 months agoWhere’s Neo in this.0

Paras Srivastav11 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 Mahale11 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.

magnanil12311 months agoWhat 4 years of engineering couldn't teach ... you did it in 2.51 minutes ❤

Mr V11 months agoHow about losing the annoying background music...?

alex Lo11 months agoI wonder when Gauss had work in matrix. Did he have this geometric description in mind?

Sa B11 months agoThis video is really great! Thank you :D

Matan Kribus11 months agoyea but what is that thing you did in the start of the video? im leanring linear algebra

ice breaker11 months agoamazing

Pumpkin11 months agoWhat can a determinant of a 4x4 dimension represent?

Jorge Mercent1 years 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 Sharma1 years 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 Duette1 years agoAl menos haberlo subtitulado al español si el título está en español ☹️

Praapthi Praapthi1 years agowhy our maths teachers does'nt know this.

ANKIT PAL1 years agoCan't get it , what are you guys doing in the beginning , are you are multiplying matrix with cube?

Sourav Mukherjee1 years 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 Khan1 years agoAmazing...

Ruolin Jia1 years agoThe person who found determinant must be a ridiculously intelligent guy.

feridun abi1 years agobut why

vijendhar bhupathi1 years agoHow transformation is made

Lv 69 Mafia Boss [MAXM]1 years agoWow good video. Watching this to get the same love I have for Calculus into Linear Algebra.

Reinaldo Maciel1 years agoPerfect explanation. Incredibly that several teachers takes more than one class to explain it (or try to) .

Patrick HotelEchoRomeo1 years 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.

Fredde1 years 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 K1 years agoAmazing video!! I never ever imagined determinants and eigenvectors this way... Thank you so much 👌👌

avinash chowdary1 years agowhy do we want to transform a cube?

Barzhikev Il1 years agoThis is so beautiful I wanna cry

matsu sumo1 years agoIs it useful only if it is Affine transformation??

alex Marshall1 years agowho was Eigen..he/she pops up regular..ie Eigentones

Srikanth kola1 years agoHow to form cube with matrix

Not understood

Pladimir Vutin1 years agoI was never taught this when we learned about determinants. We were only taught how to find one, not what it actually was.

Xav Nimportnawak1 years 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?