Changing Between Two Bases | Derivation + Example

We previously saw the "Change of Basis" formula between a nonstandard basis and the standard basis. In this video, we look at how to change between two different nonstandard bases. Indeed, we derive a single matrix, called the Change of Basis Matrix, that is simply the product of two others: converting from the B basis to the standard basis, and converting from the standard basis to the C basis. That lets us go from the B to the C directly.
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2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!
Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
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Пікірлер: 52

  • @1KosovoJeSrbija1
    @1KosovoJeSrbija14 ай бұрын

    Literally the best algebra channel on youtube

  • @jeffrey8770
    @jeffrey87703 жыл бұрын

    imo by far the best vid on youtube explaining the concept of a change of basis. I had trouble understanding this for a really long time and now all of a sudden , I do, so thank you!

  • @timavilov8712
    @timavilov87122 ай бұрын

    You are the guilty of my healthy mental state and 8hr of sleep. Thank you !

  • @kathirs1
    @kathirs15 жыл бұрын

    I am watching all your LA videos ! They're really helpful

  • @sofiachalkias5767
    @sofiachalkias57673 жыл бұрын

    I didn't understand how the change of basis matrix was a thing until you showed these formulas that my prof shorthanded during lecture. Thank you!!

  • @kiriakosriniou7122
    @kiriakosriniou7122 Жыл бұрын

    This is by far the best and most intuitive explanation on basis change.

  • @AhmedAbdelazim--
    @AhmedAbdelazim--5 жыл бұрын

    I think these series are so great! I`ll share it with my friends I hope u extend your playlists to more math branches in the future. ^_^

  • @ngilad8
    @ngilad84 жыл бұрын

    Thank you very much on this series and this particularly video. Excellent and very clear stuff.

  • @md.robiulislam1592
    @md.robiulislam15924 жыл бұрын

    Thank you so much sir. your teaching method of actual geometrical visualization is great. Everyone should follow this. I am really grateful to you.

  • @YashTrivedi21
    @YashTrivedi213 жыл бұрын

    Your videos on Linear Algebra are the best ones on KZread. Thanks. :)

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Glad you like them!

  • @ameer9672
    @ameer967211 ай бұрын

    Man i can see the passion and love of math in your eyes when you explain!THANK YOU❤!

  • @jau-minlien5532
    @jau-minlien55326 жыл бұрын

    This is the best algebraic demonstration of basis change I have ever seen.

  • @nachiket481
    @nachiket4814 ай бұрын

    Could not be any better Dr Bazett

  • @kietnguyenhung1505
    @kietnguyenhung1505 Жыл бұрын

    I have been struggling one day figuring out what the hell is going and luckily I see this video, you save me alot of times, thank you

  • @mechros4460
    @mechros44608 ай бұрын

    27k view only?? By far the best video explaining change of bases to me. After this video all kinds of derivations and applications become apparent.

  • @mostafaahmadi4998
    @mostafaahmadi49982 жыл бұрын

    Just incredible. Thank you so much.

  • @oliverle5606
    @oliverle56062 жыл бұрын

    Thank you so much. The equation just dissolved all of the fog about the changing bases within my brain

  • @pedrogaleano6722
    @pedrogaleano67223 жыл бұрын

    Great as always Mr. Bazett!

  • @learnalways8213
    @learnalways82134 жыл бұрын

    Very nice and easy way to teach thank you Sir.

  • @captainhd9741
    @captainhd97413 жыл бұрын

    Thank you. Really. This is such an amazing video, short, concise, brings reminders of how to think, you show your own reasoning, the symbols are not some confusing ai and aj type of thing, and there are examples. Keep powering through maths!

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Glad you enjoyed!

  • @ronicave8522
    @ronicave85224 жыл бұрын

    Man all your videos have helped me through all my mathy courses they are excelent

  • @sebastianramirezcaseres2965
    @sebastianramirezcaseres29654 ай бұрын

    Thanks for the explanation dr. Greetings from colombia.

  • @Tyokok
    @Tyokok Жыл бұрын

    thanks for THE GREATEST lecture!

  • @TheWeberGer
    @TheWeberGer3 жыл бұрын

    Very good explanation. Thanks

  • @swoch185
    @swoch1855 ай бұрын

    Very good expliation!

  • @WarzoneMasters
    @WarzoneMasters8 ай бұрын

    dude god bless you

  • @edisondoko9113
    @edisondoko91133 жыл бұрын

    I love this explanation

  • @petermanfield
    @petermanfield4 ай бұрын

    Love you Trefor!

  • @mohamedmouh3949
    @mohamedmouh3949 Жыл бұрын

    thank you so much

  • @matejcataric2259
    @matejcataric2259 Жыл бұрын

    very nice explanation!

  • @jay.mona.31
    @jay.mona.314 жыл бұрын

    Wow this is so helpful 👍🏻👍🏻👍🏻

  • @nayeemx11
    @nayeemx112 ай бұрын

    awesome ❤❤

  • @sukranochani5764
    @sukranochani57643 жыл бұрын

    Thankyou sir

  • @matthewsarsam8920
    @matthewsarsam89208 ай бұрын

    Whenever I have a new basis then can I always think about the new basis vectors as written in the standard basis. Essentially, can the standard basis be the “master basis” where everything can be though of through that basis?

  • @halim_Ha
    @halim_Ha4 жыл бұрын

    good good subscribed

  • @maximuz8533
    @maximuz85332 ай бұрын

    2 days of my life explained in 1 video

  • @Unidentifying
    @Unidentifying2 жыл бұрын

    im finally getting linear algebra. probably not in time for my exam but for the retake :D

  • @Imran52Feb
    @Imran52Feb2 жыл бұрын

    If inverse does not exist transformation is not possible, is it ?

  • @michaellam4082
    @michaellam40822 жыл бұрын

    If the commutativity of matrix multiplication matters for what it is, how is equation 6:15 valid? inv(Pc)*(x)b = inv(Pb)*(x)c is what I'm talking about, with inv() as the inverse notation (as in matlab command) Edit: I'd like to add tho, I never understood change of basis until I watched this video. So this was very good and your work definitely helped me understand linear algebra much better!! Thanks!

  • @asht7788
    @asht77884 жыл бұрын

    If you see, these topics are intuitive but it exposes a flaw in our education system. I should get my degree from KZread

  • @skillick
    @skillick Жыл бұрын

    Great teacher, why is he in such a rush?

  • @kjekelle96
    @kjekelle96 Жыл бұрын

    I'm kind of confused because as far as I understand this is totally inapplicable in more abstract vector spaces such as R[X]. Did you explicitly mention in the series that you're going to focus on coordinate spaces?

  • @DrTrefor

    @DrTrefor

    Жыл бұрын

    Indeed, this linear algebra playlist is intended entirely in R^n. Of course, a lot of things extend pretty similarly to other vector spaces, but that is beyond the scope of this particular series.

  • @alfcnz
    @alfcnz2 жыл бұрын

    LOL, this is *so* confusing… Haha 😅😅😅 I feel extremely rusty!

  • @PoloJust
    @PoloJust3 жыл бұрын

    hero

  • @youssefdirani
    @youssefdirani2 жыл бұрын

    The shirt button is open. Anyway, super thanks sir.

  • @Yishay.S
    @Yishay.S2 жыл бұрын

    A P(iece) of C(ake)

  • @openyard
    @openyard2 ай бұрын

    Ace of base?

  • @marcuswortmann9664
    @marcuswortmann9664 Жыл бұрын

    we all know what Pc does... checking someones privilage

  • @marcuswortmann9664

    @marcuswortmann9664

    Жыл бұрын

    and check on someones micro-aggresions