Nietzsche's Moustache Is the Best - Sadly my math is not as good as his, so I suppose that makes me a mere 'polynominal'... (I hope you read it carefully)
I just read this proof in a book earlier today. It was more generalized but it used the same idea of thinking in terms of polynomial roots. The notation was really ugly though, so this video helped to clarify the concept for me. Thanks for making your videos, you're a huge inspiration.
Currently learning it in Linear Algebra by Georgi E. Shilov. The xyz notation makes it a bit easier to understand in this video, instead of x1, x2....Xn. But in the book it's generalizing all matricies like this so I guess it's necessary.
Brilliantly and theatrically explained! If you're trying to find a cubic equation that fits 4 points (x,x'), (y,y'), (z,z'), (t,t') you get a matrix equation; taking the determinant of the matrix yields the vandermonde determinant. If (and only if) the determinant is nonzero, the matrix is invertible and you can find the cubic to fit your points. Looking at the expression, all we need for the determinant to be nonzero is x,y,z,t to be pairwise distinct.
Shannon Martens Exactly! Which also makes sense in terms of cubic interpolation: you essentially need the first coordinates of your points to be distinct in order to find a interpolation between them! As a side note, there's also a proof of the Vandermonde determinant using Lagrange polynomials, although I don't remember it any more
PackSciences Absolutely! I was gonna use the row-reduction technique first, but this approach is much cleaner! And of course I did the case n = 4 for pedagogical purposes; the general case is similar!
Not only exciting in itself, but I think I've been solving some Vandermonde matrices without realizing it. This could be really handy. Calling C C1 and then using C2 with (z-y)(z-x) then combining them all would have kept the induction idea explicit--it was perfectly clear, but there just would have been an elegance to lacing the recursions together.
Nice proof and nice translation, though "van der" is Dutch spelling before 1934, where "der" is the male genitive form of the definite article "de". Further, "van der" is equivalent to "del" in Spanish and "du" in French, which explains names as Delmondo and Dumonde, respectively. Finally, Vandermonde refers to how administration of Belgium files a composed family name, while "van der Monde" is how they do it in the Netherlands. So the name tells he is from Belgium, and has either ancestors from Spain or France.
Benjamin Segall Yes, of course! In the video I did the case n = 4 for illustrative purposes, but the exact same method works for any positive integer n.
I had to show this in my last linear algebra exam for any nxn matrix of that form, then we had to use it to show that a polynomial of n-th degree has at most n solutions, if you set it to zero
Obviously it isn't really what it is, but for continued use of matrices for vector analysis it might(so I'm just asking what is the intuition for putting (y-x) and also (z-x) there??
Marcus Sorry for the late reply; It's just a convention, it would have been perfectly acceptable to do it the other way because there are an even number of factors, so any minus signs would cancel out anyway!
Dr Peyam is so great. Very enthusiastic about math and also a polyglot!
Nietzsche's Moustache Is the Best - Sadly my math is not as good as his, so I suppose that makes me a mere 'polynominal'...
(I hope you read it carefully)
I love his enthusiasm I wish more math instructors were like this it would make math so much more enjoyable
It's so different from how my teacher taught me this and YOUR EXPLANATION IS REALLY AMAZING! Thanks alot!
I just read this proof in a book earlier today. It was more generalized but it used the same idea of thinking in terms of polynomial roots. The notation was really ugly though, so this video helped to clarify the concept for me. Thanks for making your videos, you're a huge inspiration.
Currently learning it in Linear Algebra by Georgi E. Shilov. The xyz notation makes it a bit easier to understand in this video, instead of x1, x2....Xn. But in the book it's generalizing all matricies like this so I guess it's necessary.
Dude, that eraser is so satisfactory!!! Thanks a lot for this video ^^,
The memes are strong in you, keep it up :D
I'm sooo happy you now have a chanel too. Great video!! :D
Me: "This guy is awesome, I'm going to subscribe". Also Me: "Oh I already am!"
being a student of dr peyam became a dream to me . amazing way to share knowledge keep it
I have never left a single comment on you tube till now but yours simplicity and intelligence is remarkable. Keep up the good work
Thanks so much!!
I'm just planning to watch all your videos and I want to say you that I love your personality. Thanks for everything!
dude I was given the transpose of this matrix to solve as a challenge in my school. This method is just so elegant I just love it!
I really enjoy your topics and you explanation method.
omg i have read about this in the textbook but wow, this vid is phenomenal i have to say that
Excellent video. One can enjoy mathematics in each and everyone of your videos. Thank you very much.
Brilliantly and theatrically explained! If you're trying to find a cubic equation that fits 4 points (x,x'), (y,y'), (z,z'), (t,t') you get a matrix equation; taking the determinant of the matrix yields the vandermonde determinant. If (and only if) the determinant is nonzero, the matrix is invertible and you can find the cubic to fit your points. Looking at the expression, all we need for the determinant to be nonzero is x,y,z,t to be pairwise distinct.
Shannon Martens Exactly! Which also makes sense in terms of cubic interpolation: you essentially need the first coordinates of your points to be distinct in order to find a interpolation between them! As a side note, there's also a proof of the Vandermonde determinant using Lagrange polynomials, although I don't remember it any more
Original manera de calcular el determinante de Vandermonde! Great video ;)
Wonderful work, definitely looking forward to more linear 'junk'
I have read this proof in a book and it was like eating under cooked chicken. Dr. Peyam makes it like eating ice cream.
It’s cold and it gives you cavities? 😂 Hahaha, thank you, I really appreciate it ☺️
Wow, beautiful mathematics. Thanks!!
With the family of alphas being the unkowns, you can also prove it using the operation C_i
PackSciences Absolutely! I was gonna use the row-reduction technique first, but this approach is much cleaner! And of course I did the case n = 4 for pedagogical purposes; the general case is similar!
Hahahaha. Funny ending xdddd
Amazing video. I'm loving this channel.
JaviLark01 yay!!!!!!
Peyam you are a mathemagician!
Not only exciting in itself, but I think I've been solving some Vandermonde matrices without realizing it. This could be really handy. Calling C C1 and then using C2 with (z-y)(z-x) then combining them all would have kept the induction idea explicit--it was perfectly clear, but there just would have been an elegance to lacing the recursions together.
i thought it was Voldermort :|
Nice proof and nice translation, though "van der" is Dutch spelling before 1934, where "der" is the male genitive form of the definite article "de". Further, "van der" is equivalent to "del" in Spanish and "du" in French, which explains names as Delmondo and Dumonde, respectively. Finally, Vandermonde refers to how administration of Belgium files a composed family name, while "van der Monde" is how they do it in the Netherlands. So the name tells he is from Belgium, and has either ancestors from Spain or France.
That is amazing, thank you!!!!
Yeah, it was quite obviously not the true meaning, but a very cool interpretation
Comptez-vous faire des vidéos en français? It is such a pleasure to learn maths with a teacher like you!
Oui, en effet! Il y aura une vidéo peut-être la semaine prochaine :) Et évidemment vos suggestions seront appréciées
Merci beaucoup!
pretty demonstration. Thanks.
Van Der Monde = From the moons : He's an alien :)
If it was 5*5 matrix would there be 5C2 or 10 terms in it?
It would be 1 + 2 + 3 + 4 = 10 :)
Can this be generalized to a nxn determinant with rows
a_1^0 ... a_1^(n-1)
......
a_n^0 ... a_n^(n-1)
Benjamin Segall Yes, of course! In the video I did the case n = 4 for illustrative purposes, but the exact same method works for any positive integer n.
Dr. Peyam's Show just finished working the full general form and proof out on paper. Thanks for making these videos to spark my curiosity
I had to show this in my last linear algebra exam for any nxn matrix of that form, then we had to use it to show that a polynomial of n-th degree has at most n solutions, if you set it to zero
yo dawg, i heard you like derivatives. so i put a function inside of yo function so that you can derive while you derive
AndDiracisHisProphet lolllllllll
What is the usual way? I read this proof in a book that was published 40 years ago.
There will be a video on that (which you can also find on my playlist)
Thanks. I'm very excited :-)
van doesn’t mean from
What does it mean?
Why this negative orientation for C?
Obviously it isn't really what it is, but for continued use of matrices for vector analysis it might(so I'm just asking what is the intuition for putting (y-x) and also (z-x) there??
Also; I like the show.
Maybe I know the answer to my question myself!? It just looks easier...hmm!?!
Marcus Sorry for the late reply; It's just a convention, it would have been perfectly acceptable to do it the other way because there are an even number of factors, so any minus signs would cancel out anyway!
OK!
Wonderful
Hi. Great video. Audio, not so much.
Mond means also moon in german
Yes. And Monde is the plural of Mond in german.
I did the general case here: th-cam.com/video/sd20wj2NN4s/w-d-xo.html
Math freaks, I am joking, thanks so much.
He's our "King Julian" of Mathematics!
Why so cute Dr Peyam ? lovely man
🥰
what a guy :D