Dual Basis Example

[@pythagorasaurusrex9853]

So long story short: "How to calculate the dual basis?" 1) Write your basis vectors as column vectors in a matrix. 2) Invert that matrix 3) Your dual basis vectors are the row vectors of your inverted matrix

[@javierpicazo2107]

But id you that how can you get the expression he got?

[@done7216]

Yesterday i had my linear algebra exam and i literally forgot that dual basis even existed so i didn’t learn it. 10 minutes before the exam started i quickly tried to look if someone made a short video about it but this was the only one i found and i didn’t had that much time to watch it. Then i read your comment and this was the only thing i knew about this topic. Ironically, i had to calculate a dual basis and i did it exactly like you said (it was correct). Now i got the results and i passed it very very close. Long story short: without your comment i would have failed the exam and had to redo the class next year. So thank you stranger from the internet, you saved my semester 🙏🏻

[@apolloo9068]

Three years later the video is still really useful, and it will be for years to come! Thanks for taking the time to make it.

[@marcoaraujo__]

I study mathematics at the University of São Paulo (USP), and in this quarantine time I can't go there. My course is very abstract and I have many difficulties to understand the algebraic examples. I'm practicing the English, and you helped me so much in English and maths. Thanks

[@ericluz6054]

3 anos depois, eu tô tendo algelin II com a professora Leila no IME-USP e o Dr. Peyam tá me salvando hahahahahaha

[@marcoaraujo__]

@@ericluz6054 Parabéns por ter entrado no IME!!! A Leila é um amor e o Dr. Peyam salva muito!!! No fim, percebi que boa parte dessa dificuldade com abstrações era por não ter um propósito claro na Pura e a frustração de pensar "poxa, por que to aprendendo isso?", situação essa que mudou após eu ter migrado pra Estat

[@cezarionescu75]

I'm doing my PhD and bachelor degree in physics (at the same time, long story) its nice to revisit old subjects that you taught you understood to find new ways of looking at them. I enjoyed this video a lot, will look at more of your videos and subscribe

[@drpeyam]

Thank you!!!!

[@robertbistone5366]

How do you do a PhD in physics and a bachelors in physics at the same time?

[@hansbaeker9769]

@@robertbistone5366 I knew an undergraduate math major who took just about every graduate course in math as an undergraduate and aced them. So it doesn't seem impossible for someone to do both a PhD and BS (or BA) in the same subject simultaneously.

[@valentinfontanger4962]

As a math student in quarantine, you are now my new hero

[@marcoaraujo__]

He's my hero too

[@61rmd1]

very nice and useful video; it is easily transposed on R3 (and on Rn, of course...), with, for example (210), (310), and (011) as basis. It runs without any problem

[@ambrishabhijatya7842]

0:21 "Today I wanna sort of garnish it" My man be teaching Maths like a michelin star chef cooks dishes.

[@lordexa]

I love that positivity, keep it up.

[@tgeofrey]

I love ur devine Mathematician

[@drpeyam]

❤️

[@darkseid856]

While finding f1(x,y) , you expressed (x,y) in terms of standard basis , that is , x(1,0) + y(0,1) , But why ? In the problem , it's given that beta is our basis , (2,1) and (3,1) . So why didnt we express (x,y) in terms of these basis ?

[@lynny7868]

my exact question

[@DipsAndPushups]

I didn't understand that too. Also, he said f(x,y) = 2x - 5y is arbitrary, but then he got 2x-5y by not plugging that f(x,y)=2x - 5y information anywhere. He got 2x - 5y just by picking the basis vectors to be (2,1) and (3,1). So, I don't understand how is f(x,y) = 2x - 5y arbitrary when he got 2x - 5y by only plugging in the information that basis vectors are (2,1) and (3,1) I would like to see an example of a vector expressed with bases (2,1) and (3,1). For instance, I would like to see what happens if the input vector is 11(2,1) + 7(3,1)

[@navyawhig]

ABSOLUTELY AMAZING THANKYOU SO MUCH

[@drpeyam]

❤️

[@thecarlostheory]

thx you a lot for this exercices. I´m impressed how we can discover the vector of the basis of a function.... each basis of each function must hide a very exiting natural and geometry meaning! i´m so impacient to discover that!

[@unplandsitch]

thank you so much. It seems so easy explained like this.

[@toanhocchanphuong]

Great video. thanks a lot. Could you please give a geometrical interpretation of this dual basis?

[@ETeHong]

a good practical example!

[@sumers9396]

great explanation!!

[@RB-jz1rr]

Can this problem be solved by not using standard basis, but rather the basis you used in beta? So insead of writing f_1(x,y) = (f_1(x(1,0) + y(0,1)) we would write x and y in terms of (2,1) and (3,1)

[@nickname6764]

Thanks a lot for this video!

[@KarlVilhelmssonEmneby]

Thanks so much brother!

[@hammockfinance3028]

I was looking for a video on Dual Basis Rule of taxation in the USA. I guess I'm in the wrong place.

[@rogue6343]

Incredible video

[@dgrandlapinblanc]

Interesting. Thank you very much.

[@DipsAndPushups]

Can someone show me what happens if the input vector is 11(2,1) + 7(3,1)? Can someone calculate it please and show me the steps? I think that will help me clear things up a bit

[@BlackanBlue00]

Thank you this is very helpful

[@xichengtang584]

Hi Dr. Peyam, I have a question about dual space. Suppose we have vector space U = P2, polynomials with degree up to 2. How do we use dual basis to express functional f(p(t)) = p(6)?

[@drpeyam]

It’s in the playlist :)

[@ThemJazzyBeats]

Didn't we just end up computing the inverse of the matrix that has the 2 basis vectors of V as rows ? It seems that the 4 coefficients we solved for ---> f_1(1,0), f_1(0,1), f_2(1,0) and f_2(0,1), are respectively -1, 3, 1 and -2. If we organize (-1,3) as the first column of a matrix and (1,-2) as the second, than that matrix is precisely the inverse of the matrix containing the 2 basis vectors of V as columns. This CANNOT be a coincidence

[@drpeyam]

You’re right, it’s not a coincidence and it’s precisely because of what you said!

[@ThemJazzyBeats]

@@drpeyam We end up inverting because of the canonical basis that forms the identity matrix right ?

[@drpeyam]

Basically yes

[@oli7908]

Thank you for this video

[@NAMEhzj]

Hey Dr. Peyam, cool stuff, but you probably didn't want ppl to see this yet right? (since it isnt listed) It can be seen on the dual spaces playlist right now.

[@drpeyam]

I do want people to see it, in case they’re curious (and for my students), but I’ll release it on Saturday

[@NAMEhzj]

@@drpeyam Ah I see :)

[@highermathematics6494]

B= { 1, x, x^2} how to solve dual basis

[@drpeyam]

It would be {f1,f2,f3}, where f1(a+bx+cx^2)=a, f2(a+bx+cx^2) = b etc.

[@highermathematics6494]

Pls solve this one?

[@drpeyam]

That’s the solution...

[@Ixam13]

Thanks mate!

[@sajidhaniff01]

Thanks so much!

[@santiagogomezpu]

Wonderful!

[@nelsondavidcarbajalcusi9955]

I love you

[@wiloux]

Nice

[@xnorgate5894]

Um, I'm new here, I just can't figure you out bro. You sound arabic and german at the same time, look indian, what exactly are you?

[@drpeyam]

I’m Persian but grew up in Austria and moved to the US when I was 16 :)

[@sanelprtenjaca9776]

Please make video in croatian. It is year after historical World Cup 2018 🗺⚽️🇭🇷

[@Л.С.Мото]

Croatia lost, so he would have to do it in french

[@sanelprtenjaca9776]

@@Л.С.Мото No, no. Croatia won our hearts