Introduction to the null space of a matrix | Vectors and spaces | Linear Algebra | Khan Academy

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  • เผยแพร่เมื่อ 29 ต.ค. 2024

ความคิดเห็น • 63

  • @equivocal20
    @equivocal20 10 ปีที่แล้ว +241

    I just donated $10 to the Khan Academy. I wish I could donate my full tuition to you, as you deserve it more than my university, but I gave you what I could afford. Thank you so much, Sal!

    • @sarnousfn1028
      @sarnousfn1028 ปีที่แล้ว +11

      did you graduate bro?

    • @johnli7754
      @johnli7754 ปีที่แล้ว

      0:23 0:25 0:26 0:27 0:28 0:28 0:28 0:29 0:29 0:29 0:29 0:29 0:29 0:30 0:30 0:30 0:31 0:31 0:31 0:31 0:31 0:32 0:32 0:32 0:32 0:35 0:37 0:38 0:38 0:39 0:39 0:39 0:39 0:40 0:40 0:40 0:40 0:41

  • @TTbambam13
    @TTbambam13 9 ปีที่แล้ว +22

    Wow Sal ten thousand times better explained than any of my professors at Imperial, really man If I could I would donate my whole tuition to Khan Ac
    Awesome TED talk by the way!!!!!

    • @mostinho7
      @mostinho7 8 ปีที่แล้ว

      +TTbambam13 Holy shit! you go to imperial college london?

    • @TTbambam13
      @TTbambam13 8 ปีที่แล้ว +3

      +Mostafa Adel Yeap! well.. where I really go to at the end of the day is Khan Ac!

    • @matthewsetiawan5684
      @matthewsetiawan5684 3 ปีที่แล้ว

      @@TTbambam13 what a coincidence, I also go to Imperial just had my lecture on nullspaces then went here. xd

  • @sadiaaa1373
    @sadiaaa1373 11 หลายเดือนก่อน +1

    My professor is actually good, but i was behind in class when this lesson was taught. Learning it for the exam now and this saved meeee. Thank you so much again Khan Academy!

  • @jingyiwang5113
    @jingyiwang5113 ปีที่แล้ว +3

    Thank you so much for this amazing video! I am grateful for your help with my mathematics!

  • @opmike343
    @opmike343 14 ปีที่แล้ว +43

    My linear algebra professor never does examples. All theory, every lecture, every time. Exams are usually a huge question mark going in, as we don't know what to expect. And he doesn't "like" our textbook, so he doesn't look to pull questions from there. He makes his own. Sucks.

    • @InzaneFlippers
      @InzaneFlippers 4 ปีที่แล้ว +3

      Same for me... And never gives us the anwsers to the questions either so it feels pointless to do them

    • @happyjohn1656
      @happyjohn1656 ปีที่แล้ว +1

      @@InzaneFlippers This seems like something you should be able to complain about
      4:50 AM
      5/5/2023

  • @RossRocks07
    @RossRocks07 12 ปีที่แล้ว +5

    I watch these videos BECAUSE he explains it slowly and thoroughly. If it's too slow, forward the damn video!

  • @A-003
    @A-003 14 ปีที่แล้ว +2

    God Bless You

  • @CreamO92
    @CreamO92 12 ปีที่แล้ว

    Skip lecture and listening to this is even better than wasting your time waking up early in the morning just for the god damn Eng. Maths Lecture.

  • @ekdkseho
    @ekdkseho 4 ปีที่แล้ว +3

    Distributive property of Matrix dot vector product should have been proved first for 'closed under addition' proof.

  • @danielgonzalezisaiev9643
    @danielgonzalezisaiev9643 11 ปีที่แล้ว +8

    To all people out there who I know are scratching their heads, let me lift a burden off your shoulders; Nullspace and Kernel is the same thing!

    • @Suckmyballs4733
      @Suckmyballs4733 4 ปีที่แล้ว +1

      yeah i assumed they were thank you so much now I don't have to watch the video

  • @USAACbrat
    @USAACbrat 7 ปีที่แล้ว +1

    each has a different frequency and operates within band with , annd moves on common frequinces

  • @mtdaugherty
    @mtdaugherty 15 ปีที่แล้ว +3

    These are awesome. Hoping for more soon :).

  • @wiibird
    @wiibird 14 ปีที่แล้ว

    you saved my day!

  • @EmbracingTheNow
    @EmbracingTheNow 3 ปีที่แล้ว

    Too good

  • @mariamA240
    @mariamA240 13 ปีที่แล้ว +12

    exam in 4 hours

    • @excalibercuberdavid4681
      @excalibercuberdavid4681 3 ปีที่แล้ว +3

      Bruh, how's life after college? Im a college student in 2021, so I'm quite curious

    • @dd-iy7jw
      @dd-iy7jw 2 ปีที่แล้ว

      hopefully you did well

  • @weathercircle
    @weathercircle 10 ปีที่แล้ว +1

    What do you mean by; "Closed under addition" or "Closed under multiplication"?

    • @Peter_1986
      @Peter_1986 9 ปีที่แล้ว +4

      He means that you are "stuck" inside a space and cannot get out of it either by adding or multiplying the vectors that are members of that space.
      For example, if you have two column vectors with 3 elements, and the third element is 0 in both of them, then you can never add them or multiply them in any way that changes the third element into something else than 0 - so those vectors will always have a 0 as the third elements.
      One example of a subspace is a 2D-plane in a 3D-space.
      Of course, since you are able to multiply the vectors with any number, a subspace must also include the zero vector.

    • @yousorooo
      @yousorooo 9 ปีที่แล้ว

      That means by adding or multiplying you won't leave the vector space.

  • @SomethingSoOriginal
    @SomethingSoOriginal 12 ปีที่แล้ว +1

    Sal, can you start to add speed to the videos so we can watch it quicker and save time? Thanks.

  • @HappyNadia_S
    @HappyNadia_S 11 ปีที่แล้ว

    I think your videos are good, and they do explain. I think they would be much better if you did a couple run-throughs or had written down what you wanted to say. For example, you say you will set up the homogeneous equation, then you say you will talk about why it's HMGN, then you say, well I'll tell you in a second. That's unnecessary repetition that makes the videos seem longer than they are. I end up forwarding through about half of all your videos. Keep you the great work.

  • @SomethingSoOriginal
    @SomethingSoOriginal 12 ปีที่แล้ว +2

    umm no. Clicking 10 times on each vid to skip 3 secs each time then going back cos i skipped to far etc.. is just a hassle. If i am taking notes as well then 2x speed is so much easier.

  • @gincoopland6545
    @gincoopland6545 9 ปีที่แล้ว +3

    I don't understand... Av1 = 0 and Av2 =0 then A( V1 + V2) = AV1 + Av2 isnt that only true if you take v1 and v2 to be the zero vector?

    • @Triplechoco52
      @Triplechoco52 7 ปีที่แล้ว

      If I'm following what you're saying correctly, doesn't he already say that when he mentions:
      "V1, V2 [- (that's the 'element'/pitchfork symbol) N", where N is every "x" vector that will make the statement "[A]x = 0-vector" true?

    • @damian.gamlath
      @damian.gamlath 6 ปีที่แล้ว +1

      I think not necessarily...
      If the numbers are right, then when you multiply a matrix * vector (A*v1) the result can be zero vector *_even though_* the vectors themselves are *_not_* zero vector.
      Example:
      Matrix:
      [1, -3, -2]
      [-5, 9, 1]
      Vector:
      [5]
      [3]
      [-2]
      Multiply together and we get zero vector.

  • @junkeychan
    @junkeychan 12 ปีที่แล้ว

    kernel is some what same as nullspace

  • @Waranle
    @Waranle 15 ปีที่แล้ว

    Thank you Sal Keeeeeeeep coming

  • @dfsfklsj
    @dfsfklsj 11 ปีที่แล้ว

    I see... So it is the vector set that maps the matrix to the zero vector. Very deep concepts are they not?

    • @damian.gamlath
      @damian.gamlath 6 ปีที่แล้ว

      I read on mathstackexchange.com: "Physical meaning of null space"
      the null space is like the set of vectors that _get_ mapped to the zero vector _by_ the matrix! Like with linear transformations they say.
      These concepts provoke deep thought indeed.

  • @dawsonoo7
    @dawsonoo7 13 ปีที่แล้ว

    awww fun!.. this brings back memories! good explaining also

  • @oneinabillion654
    @oneinabillion654 5 ปีที่แล้ว +1

    I was so bored after my A levels that I subconsciously began to make an expression for the number of vectors in a subspace.

  • @TheJrperks1211
    @TheJrperks1211 9 ปีที่แล้ว +14

    This video would be MUCH better if he actually found the null space.

    • @TheJrperks1211
      @TheJrperks1211 9 ปีที่แล้ว +8

      ooops wrong video my bad. This one actually helped a lot

    • @drdin3442
      @drdin3442 6 ปีที่แล้ว +1

      lolol thanks for the laugh!

  • @bwag34
    @bwag34 14 ปีที่แล้ว

    I am not worthy of your awesomeness

  • @Phagocytosis
    @Phagocytosis 11 ปีที่แล้ว +1

    Except when you do that, you may miss things. Just because you like to watch a video with things explained slowly and thoroughly doesn't mean everybody else should, does it? I for one can focus a lot better when I play it at 1.5 or 2 times the speed.

  • @HappyNadia_S
    @HappyNadia_S 11 ปีที่แล้ว

    I have to agree with Something so Original, he repeats himself a lot. Sure I forward, then I have to go back to see what I missed. It would be helpful if he was not so all over the place with his thoughts.

  • @MrCalhoun556
    @MrCalhoun556 14 ปีที่แล้ว

    @mbueno Especially when you're primarily not studying mathematics.

  • @rebiualbo2234
    @rebiualbo2234 11 ปีที่แล้ว

    So what is kernel?

    • @damian.gamlath
      @damian.gamlath 6 ปีที่แล้ว +1

      It has the same meaning as Null space _in this case_.
      But Kernel is a more "general" term in maths that applies to other concepts besides subspaces.
      But if somebody asks "Find the kernel of a matrix" they are basically saying "find the null space of a matrix"

  • @Bartolitz
    @Bartolitz 14 ปีที่แล้ว

    @mbueno My too :/
    Thanks a lot!! The videos are very helpfull

  • @nadeemdanish1868
    @nadeemdanish1868 11 หลายเดือนก่อน

    is it related to IMRAN KHAN??

  • @jovas14rocks
    @jovas14rocks 11 ปีที่แล้ว

    example please!

  • @Xlaxsauce
    @Xlaxsauce 11 ปีที่แล้ว

    don't understand why the two terms exist then

  • @tahancan
    @tahancan 6 ปีที่แล้ว

    what

  • @saibaaburein8588
    @saibaaburein8588 4 ปีที่แล้ว +1

    gg

  • @BoQuan22
    @BoQuan22 12 ปีที่แล้ว +1

    um... just skip through it then? dafuq...

  • @poesiat1
    @poesiat1 12 ปีที่แล้ว +1

    *homogeneous

  • @abrarmahi
    @abrarmahi 3 ปีที่แล้ว

    1.25x speed, thank me later