Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy

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  • Опубліковано 1 гру 2024

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  • @Powd3r81
    @Powd3r81 12 років тому +55

    I can't tell if this video is a good one or not. Linear Algebra just became so freaking hard and none of the math makes any sense. All these vector spaces and sub spaces are so abstract ughhhhh

    • @spag5296
      @spag5296 5 років тому +5

      7 years later, I'm feeling the same way! although the video was explained much better than my lecturer.

    • @aminem4626
      @aminem4626 5 років тому +2

      I feel you haha

    • @baluandhavarapu
      @baluandhavarapu 2 місяці тому

      I can assure you, the video is a good one 🤩🤩
      He could've taken a little more time and explained each algebraic step he did. But he just stuck to the kernel part of it alone, in this specific video

  • @razberrycreme
    @razberrycreme 12 років тому +11

    How are you such an amazing teacher, seriously. It would also be really helpful if you numbered your videos so that we know what order to watch it in. but seriously these are amazing. thank you!!!!!

  • @Bomberofdoom
    @Bomberofdoom 14 років тому +8

    SO THAT IS THE NULL SPACE!!!!! :-O
    Why couldn't they explain this at the same time they explained us about the null space?!?!?!
    Now that I VISUALLY see it, I can really understand what we're talking about!
    Thanks Sal!!

  • @thomasvitale5250
    @thomasvitale5250 9 років тому +11

    At 0:13 when he coins the term "multiplation" :)
    Muchas gracias Khan Academy brothas! Your videos are helping me through grad school! Who needs professors on tenure anyways :)

  • @linkwigger
    @linkwigger 14 років тому +1

    Great explanation of the nullspace of T.

  • @grandorottcod1
    @grandorottcod1 10 років тому +10

    kernel== nullspace

  • @Sheeeeshack
    @Sheeeeshack 9 місяців тому

    Little hair splitting: Kernel is a kind of transformation. It’s not all the vectors. That is basically the difference with NULL.

  • @farmerdave4000
    @farmerdave4000 8 років тому

    Thanks for the explanations!

  • @debendragurung3033
    @debendragurung3033 7 років тому

    13:16 bookmark, a set of vectors in one domain gets mapped to just a single set in range. Yet still a linear trasforation..... neat

  • @Waranle
    @Waranle 15 років тому

    Thank you Sal

  • @s0m0c
    @s0m0c 13 років тому

    Gracias!

  • @ad2181
    @ad2181 15 років тому

    thank you

  • @abhishekagrahari1007
    @abhishekagrahari1007 12 років тому

    great explanation

  • @xybersurfer
    @xybersurfer 14 років тому

    good explanation

  • @gubby740
    @gubby740 6 років тому

    thx

  • @Zmunk19
    @Zmunk19 5 років тому

    does this have anything to do with the kernel trick in support vector machines? (machine learning)

  • @spaceteapot
    @spaceteapot 12 років тому

    does he mean the space spanned by the vectors S? because S itself is not a subspace.

  • @floyd617
    @floyd617 14 років тому

    i thought it would be shifted one up, how is it to the right?

  • @DJDKCR
    @DJDKCR 8 років тому +2

    I like to skip ahead and watch these advanced videos so that I can see what I will be able to understand someday.

  • @rainerrustenberg3824
    @rainerrustenberg3824 10 років тому

    I just wonder, that if you will combain the equations at time 7:45 it wil be a contradiction.
    Why, because: x1 = -3t and, ( x1 - 1 = 3t, gives x1 = 3t + 1), so ( x1 = -3t AND x1 = 3t = 1), but that is when solving 2 linear equations with 2 unknown, sorry, I'am bad. But it sure is a great video, very well. Rainer

  • @haythemoldaccount7953
    @haythemoldaccount7953 3 роки тому

    I am doing this freshman year help

  • @devilpizza123
    @devilpizza123 13 років тому

    lol multiplation :D