Vector transformations | Matrix transformations | Linear Algebra | Khan Academy

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  • Опубліковано 7 вер 2024
  • Introduction to the notion of vector transformations
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    Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
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КОМЕНТАРІ • 41

  • @InsaneBastardGuy
    @InsaneBastardGuy 6 років тому +53

    Sal, you're my function to success.

  • @jazerazo
    @jazerazo 14 років тому +5

    Thanks a lot!! Knowing that a ''Transformation'' is just a fancy way to call a especial kind of functions makes so much easy the understanding of Linear Algebra texts...

  • @Frappuccino2124
    @Frappuccino2124 5 років тому +7

    3:13 ... Whats that pokemon? It’s Ditto!! 😊

  • @fevenjoshuacarpe1444
    @fevenjoshuacarpe1444 8 років тому +6

    Sal, i always learn something when I watch you guys

  • @walktroughman1952
    @walktroughman1952 4 роки тому +11

    Aight, my journey to become accelerator starts here

    • @ratie2573
      @ratie2573 3 роки тому +1

      SAME BRO I THOUGHT IM THE ONLY ONE

    • @samuraijosh1595
      @samuraijosh1595 3 роки тому +1

      The anime accelerator? Haha

  • @desxse6309
    @desxse6309 5 років тому +4

    Thanks Thanks, helps me a lot more than in the school and on the book.

  • @jishuenkam
    @jishuenkam 14 років тому +4

    you just mapped a complex subject into something everyone can understand ;) sweet

  • @DillonRedding
    @DillonRedding 14 років тому +4

    Holy freakin' crap!
    Thank you! It all makes sense now. The "Transformation" has been throwing me off so much in Linear Algebra.

  • @amandafalke7670
    @amandafalke7670 Рік тому +1

    Amazing. Thank you for all you do, Sal!

  • @aljoneldimaguila3234
    @aljoneldimaguila3234 4 роки тому +7

    I came here because of anime character (Accelerator from A certain Magical index or Scientific Railgun)

  • @M0vir
    @M0vir 6 років тому +1

    Thank you so much, Sal.

  • @CabCallawayMusic
    @CabCallawayMusic 6 років тому +2

    Around 5:38 he gives an example where he defines the codomain as a "subset of Rm". Wouldn't this just be the overall set of Rm? Since the range is the subset that actually gets mapped to, wouldn't any value be in the full set of Rm?

  • @christianwireko5871
    @christianwireko5871 6 років тому +2

    You did it again. Beautiful explanation. Thank you God Khan!

  • @NXTstorms
    @NXTstorms 10 років тому +4

    Could you make a video on the rodriguez transformation?

    • @nomansvlog264
      @nomansvlog264 5 років тому

      Ik it’s been 5 years but don’t think he did one yet

    • @abubakarali6279
      @abubakarali6279 4 роки тому

      @@nomansvlog264 even after 6 months.

  • @subratkumarsahoo4849
    @subratkumarsahoo4849 6 років тому +1

    Nailed it!

  • @suzuyure
    @suzuyure 8 років тому +1

    Thank you for posting this amazing video!!

  • @MasalaMan
    @MasalaMan 7 років тому +1

    This is trippy!!

  • @planthax
    @planthax 13 років тому +1

    Sorry if im wrong or if its to obvious, at 13:17 did you mean ... plus 2x2 when you wrote 2x1?

  • @fuckooo
    @fuckooo 13 років тому +1

    @dunrunan Yep, I've yet to find a good linear Algebra text book...

  • @jonathanidam8595
    @jonathanidam8595 2 роки тому

    Not too convinced! Does this topic relate with linear transformation in maths ??

  • @s0m0c
    @s0m0c 12 років тому +1

    Gracias.

  • @Waranle
    @Waranle 15 років тому +1

    beautiful!

  • @battlewarrior11
    @battlewarrior11 14 років тому +1

    incredible

  • @dorky1364
    @dorky1364 3 роки тому +2

    I came here to get my Masters in electronic and electrical engineering.

  • @MartyMacFry
    @MartyMacFry 15 років тому +1

    awesome

  • @Rahul-yu3ro
    @Rahul-yu3ro 6 місяців тому

    8:30 (personal timestamp)

  • @yjl900315
    @yjl900315 11 років тому +1

    love u!!!

  • @Flopsaurus
    @Flopsaurus 12 років тому +1

    Hey Sal, at 13:15, you wrote that the transformation equaled (x1+2*x1,3*x3) when I think you meant (x1+2*x2+3*x3)

  • @metalking0206
    @metalking0206 15 років тому +1

    great!!

  • @izi2bhappy
    @izi2bhappy 14 років тому +1

    delicious!!!

  • @cortek123
    @cortek123 7 років тому +1

    hey does anyone know what drawing program he is using?

    • @Nobody-Nowhere-Nothing
      @Nobody-Nowhere-Nothing 7 років тому +2

      Nahele Gudmundsen From what I read on the wiki, he uses an application called smoothdraw and the drawing program ArtRage. Also from his older videos (around 2008), he used Microsoft paint to make his videos.

    • @cortek123
      @cortek123 7 років тому +2

      GreenDemon125 hey thanks, super helpful!!!

    • @Nobody-Nowhere-Nothing
      @Nobody-Nowhere-Nothing 7 років тому +1

      Nahele Gudmundsen You're welcome my man.

  • @DeluxeWarPlaya
    @DeluxeWarPlaya 13 років тому

    5:25 "then we say your fucktion is vector valued"

  • @jaakkokuu
    @jaakkokuu 15 років тому

    mathematics - english - mathematics