The Null Space & Column Space of a Matrix | Algebraically & Geometrically

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  • Опубліковано 23 гру 2024

КОМЕНТАРІ • 45

  • @alkankondo89
    @alkankondo89 6 років тому +36

    Your lectures are very complete and thorough, especially with the supplementary visuals you include! This particular lecture was a great review for me for a lot of the abstract concepts of Linear Algebra that I was fuzzy on. With all the pausing and mental reviewing I was doing, it took me easily half-an-hour to get through this 10-minute video, haha!

    • @sollinw
      @sollinw 4 роки тому

      thought it was only me!

  • @stevehof
    @stevehof 5 років тому +26

    When you love a youtube series so much that you watch more than 60 videos in 2 days. I, in fact, tutor linear algebra and this series has completely reshaped how I'll introduce certain concepts, and the order I'll introduce those concepts in. Hands down the best introduction to linear algebra youtube series in existence.

  • @veggieveggie1215
    @veggieveggie1215 9 місяців тому +3

    why is this man so good at teaching

  • @manuelkarner8746
    @manuelkarner8746 3 роки тому +8

    i cant stop binging this series, I get so many dopamine kicks from every aha-moment, like very 30seconds, it´s funny

  • @AlePreludioFinal
    @AlePreludioFinal 6 років тому +6

    These videos are pure gold.

  • @eliasgibson2878
    @eliasgibson2878 7 днів тому +1

    You're a superhero who will save me on my final exam

  • @shivkarj1456
    @shivkarj1456 4 роки тому +6

    Thank you so much for your amazing tutorials. Linear algebra is so interesting when you explain it.

    • @DrTrefor
      @DrTrefor  4 роки тому +3

      Glad you like them!

  • @nhupham8127
    @nhupham8127 3 роки тому +5

    At 0:29, T(x) = [1 0; 1 0]*x
    The second column should be (0,1) instead of (1,0).
    Your video is greatly comprehensive; everything is good except the mistake of the second column I mentioned above.

    • @elfabri666
      @elfabri666 3 роки тому +4

      No, the matrix shown in the video is right. Notice that both columns are the same vector, (1,0), and that is why it spans the x-axis. If we have Ax=b, with x any vector from IR^2, let's say (a,b), a,b real numbers, then Ax=(a+b,0). You'll understand this idea better when you have a notion about a space generated by a set, the rank of a matrix and its dependenciy. Hope it helps :)

  • @rotarydev3891
    @rotarydev3891 4 роки тому

    You are a legend! Seriously your videos help me tremendously and I would struggle far more without you. So thank you very much!!

  • @maxwellchiu9934
    @maxwellchiu9934 Місяць тому +1

    I often come here when I have questions about something I see in 3Blue1Brown. This was very helpful.

  • @bill7064
    @bill7064 4 роки тому +3

    The visualisation in this video is very helpful. Than you :)

  • @maurocruz1824
    @maurocruz1824 6 років тому +8

    Your particular vision of this stuff is amazing. Is there a geometrical meaning for the row space as well?

  • @fotisrokanis4919
    @fotisrokanis4919 6 років тому +4

    .
    The idea to represent geometrically linear algebra was awesome. Linear algebra is (rightfully) taught in an abstract manner, but usually to first year students who are not used to the abstractness of pure math. Are you going to make a video on quotient vector spaces?

    • @fotisrokanis4919
      @fotisrokanis4919 6 років тому

      Trefor Bazett It does. I study mathematics, with most of my courses in pure ones (Next year will be topology, abstract algebra II, differential geometry II ect).If I can help you in any way (prepare notes for a video for example) l'd be glad to do so

  • @abdallahalsahhar9511
    @abdallahalsahhar9511 4 роки тому +2

    amazing lesson, Thanks for time and effort

  • @jan-willemreens9010
    @jan-willemreens9010 2 роки тому +2

    ...Crystal clear lecture, Dr. Trefor... Thank you very much.

  • @shafiqshams3065
    @shafiqshams3065 4 роки тому +6

    This is so amazingly explained but still its really hard to get it completely.

    • @DrTrefor
      @DrTrefor  4 роки тому +7

      I agree, this concept really needs you to sit down and wrestle with it for a while and come back to the video after doing that

  • @Compassrome27
    @Compassrome27 4 роки тому

    Thank you so much sir. Saying your work is an amazing piece is just such an understatement. Over here you don't just present mathematical concepts with utmost clarity but also with burning passion. You are a legend 👍

  • @sakcee
    @sakcee 5 місяців тому

    Excellent!

  • @advancedappliedandpuremath
    @advancedappliedandpuremath 7 місяців тому

    Hi Sir how can we find the null space of set of vectors from M2x2

  • @DemiHalf
    @DemiHalf Рік тому

    0:39 Im pretty sure one can easily find a vector that does not collapse to the x axis when multiplied by that... Right...?

    • @mathrovert
      @mathrovert 11 місяців тому

      The b vector (after transforming vector x) would be < x_1 + x_2 , 0 > Your 2nd component is zero.

  • @raginibhayana8305
    @raginibhayana8305 3 роки тому

    how do you plot the matrixes on the graph?

  • @sergiolucas38
    @sergiolucas38 2 роки тому +1

    Nice video, thanks :)

    • @DrTrefor
      @DrTrefor  2 роки тому +1

      Glad you liked it!

  • @gate_dose
    @gate_dose Рік тому +1

  • @huychaungoc830
    @huychaungoc830 4 роки тому

    if A is a square matrix, Does Null(A) = Null(A^2)? please help me

  • @mardzj
    @mardzj 4 роки тому

    6:58 Subsets of Rm or Rn?

    • @mardzj
      @mardzj 4 роки тому

      I don't understand why in one case it should be n and the other m

    • @mardzj
      @mardzj 4 роки тому

      @@DrTrefor thank you!

  • @HeyEveryoneHi
    @HeyEveryoneHi 4 роки тому

    What the hell? I just watched five videos on linear algebra and now I understand it! Without even taking the linear algebra course

  • @dhananjayjoshi3561
    @dhananjayjoshi3561 4 роки тому

    Will you please explain row space in the same manner

    • @dhananjayjoshi3561
      @dhananjayjoshi3561 4 роки тому

      @@DrTrefor thankyou very much. We would love to watch more videos on linear algebra as well as real analysis.

  • @AbjSir
    @AbjSir 10 місяців тому

    Thanks

  • @yihongli7252
    @yihongli7252 2 роки тому

    你是我的神!!!!!

  • @anilsharma-ev2my
    @anilsharma-ev2my 4 роки тому

    Whole universe is a matrix amd god is its determination factor which is zero solution for it's original position and equation for systems equation of all types🤓🕉🕉🕉

  • @zegervg8152
    @zegervg8152 2 роки тому

    merci wi matje ma paul igodt legt et beter ut

  • @kmishy
    @kmishy Місяць тому

    most videos just talk about mathematics...you talked about logic and why

  • @sollinw
    @sollinw 4 роки тому +2

  • @SS-pl7ci
    @SS-pl7ci 2 роки тому

    No enough examples.. very abstract.