5.4 - Eigenvectors and Linear Transformations

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น • 23

  • @joeyhomeier87
    @joeyhomeier87 2 ปีที่แล้ว +13

    Great video! You used the examples right out of the text book I'm using but explained the solutions so much clearer than the textbook could do!

  • @olivier306
    @olivier306 3 ปีที่แล้ว +4

    This was exactly what I needed to see, thanks!!

  • @jonathancamarena3117
    @jonathancamarena3117 ปีที่แล้ว +4

    Whish I found these at the start of the semester.

  • @Winchester_1967
    @Winchester_1967 2 ปีที่แล้ว +5

    I don't understand how you got the vector (0, 2, 0) (16:11)

    • @njalpedersen
      @njalpedersen ปีที่แล้ว +2

      It is because the vector has the values [ number, t , t^2 ], and since t^2 after the transformation is 2t. then the vector will be (0, 2, 0). For example if t^2 after the transformation would be 2t^2 then the vector would be ( 0, 0, 2) but it wasn't

  • @matthewzarate8851
    @matthewzarate8851 11 หลายเดือนก่อน +7

    This has been the most unintuitive section of the linear algebra book so far

  • @colegreenfield219
    @colegreenfield219 4 ปีที่แล้ว +2

    at 11:40 you say T relative to B but write T relative to T. I could be incorrect but wouldn't the subscript be a B?

    • @paulcartie3820
      @paulcartie3820  4 ปีที่แล้ว +3

      Yes, absolutely - that should be a subscript of B. Good catch.

  • @Elijah_Hoenig
    @Elijah_Hoenig ปีที่แล้ว

    Fun fact extension: In base twelve, the number 321' is the smallest prime number of that form since 21' = 5 x 5. The smallest base where 21 is prime is base three, convinetly the smallest base where 2 is a digit.

    • @paulcartie3820
      @paulcartie3820  ปีที่แล้ว

      I appreciate your fun fact extension. Thanks for sharing.

  • @tech_science_tutos4155
    @tech_science_tutos4155 4 ปีที่แล้ว +1

    thanks, could you plz send me book title of this course

    • @paulcartie7095
      @paulcartie7095 4 ปีที่แล้ว +2

      Hi, the text is Linear Algebra and Its Applications, 5th Edition, by Lay.

  • @eswyatt
    @eswyatt 2 ปีที่แล้ว +1

    My confusion is I can't help but think of "T" as "designed" to work properly on basis B or basis C, but not both. I guess if it's "designed" for a basis it must be the standard basis, i.e., i, j,k.

  • @nicholaspisano37
    @nicholaspisano37 ปีที่แล้ว

    In an serious note, does that mean applying an any operator to a function is, in a sense, applying a linear transformation?

    • @paulcartie3820
      @paulcartie3820  ปีที่แล้ว

      That does seem to be the case, yes.

  • @sarahstets
    @sarahstets 7 หลายเดือนก่อน

    That was actually really cool but also odd for the start of the video fun fact…why only 82…

  • @YasinFarid04
    @YasinFarid04 8 หลายเดือนก่อน

    Very interesting and confusing topic at the same time. Beginning of the video was more confusing than the rest.

  • @adamjahani4494
    @adamjahani4494 5 หลายเดือนก่อน +1

    I'm taking applied linear algebra in the summer and we have 5 weeks to learn everything. I was going to drop but it was a day later before I could. Test every week and 2 quizzes every week. This is such a horrible way to learn math...

  • @nicholaspisano37
    @nicholaspisano37 ปีที่แล้ว

    My immediate question is how high did your coworker check?

    • @paulcartie3820
      @paulcartie3820  ปีที่แล้ว

      I think he check up to 500499...321. But as far as I am aware, no number exists other than the one I talked about that is not prime.

  • @devrimpacal4406
    @devrimpacal4406 7 หลายเดือนก่อน +1

    this is hard to understand for non math majors. im an engineering major and i had a really hard time understanding this.

    • @YusufEmreMUŞTU
      @YusufEmreMUŞTU 7 วันที่ผ่านมา

      gectin mi lineeri devrim

    • @devrimpacal4406
      @devrimpacal4406 7 วันที่ผ่านมา

      @ Byle gectim kanka ama bu adamdan izleme