a beautiful determinant derivation

intuitive derivation of the determinant

In this video, I give a really intuitive derivation of the determinant, based on some simple geometry. A huge shout-out to Loic Etienne, who suggested this proof.

[mastershooter]

I love the fact that he says "thanks for watching" at the start of the video

[MrCigarro]

Genial, preciosa y precisa demostración. Gracias por su excelente video.

[bronkolie]

I figured it out by myself at around 3:36. All the other videos never really explained how the formula they got actually correlated to to the area of a parallelogram. When I tried to derive it on my own I ended up trying to use trigonometry and Pythagoras, to little success. Thanks for the explanation!

[kee]

Thanks a lot for your video that make determinant (mathematics)became more visual!

[agustinsaenzanile]

So nice that the matematics is after the notation, beautiful

[FlydingVent]

Great video, i wanna see something like this for 3x3 matrices

[mohammedal-haddad]

Geometry-based proofs are my favorite. Thank you very much.

[andrewthompson]

That’s was quite beautiful air! Thanks for showing that :)

[MrRyanroberson]

funny enough 6:00 this follows into vector mathematics! if you label point (a, b) = A and point (c, d) = B, then you have reinvented the formula for the signed area of the parallelogram spanned by two arbitrary vectors, AxB. and this works in general for any lines since you would first shift the bottom-left vertex to the origin before doing this calculation

[friedrichfreigeist]

Lustig, dass ich sowas schon in der Realschule machen durfte. Dabei kommt Lineare Algebra erst in der Uni richtig dran. Nur damals konnte man eben nichts vonwegen Vektorräume und so machen. Man hat die Determinantenformel lediglich benutzt.

[brendanlawlor]

wot a beauty . geometric determinant didn't know it's geometric thanks Doc !! 😀

[atahualpaarias]

Cool demonstration and funny jokes, thanks!

[wuyqrbt]

Hello Dear Dr Peyam
It was so cool, thank you for sharing this with us.

[رضامزوز-خض]

Sir, I heard that if we take a square whose side length is 1 and start dividing it, then the two sides are calculated, then I find the result of 2, but when I reach infinity I find √2

[rarebeeph]

so if you have a 2x2 matrix containing a, b, c, and d, then the determinant is just the area of any parallelogram with vertices at (0, 0), (a, b), and (c, d)?

[rigoluna]

Nice video as always. Could this method be used to find the determinant of a 3x3 and or a 4x4?

[eduardvalentin]

can this be proven using the cross product?( |axb| )

[calendar]

Ah yes, nowadays, whenever I see a triangle and a parallelogram in the same parallels like that, I always refer to the Euclid's elements book 1 proposition 41 (if I'm not mistaken) about the matters.

[theamazingworldofgusball]

Is there some proof of formula for n×n matrix determinant?