Derivative in a box

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  • เผยแพร่เมื่อ 22 ธ.ค. 2024

ความคิดเห็น • 20

  • @martind2520
    @martind2520 5 ปีที่แล้ว +32

    And of course the matrix is not invertible...
    Which proves that integration doesn't exist.
    QED

    • @ajokaefi
      @ajokaefi 4 ปีที่แล้ว +1

      Not that it does't exist but that it is not unique, ... in fact it is a subspace, ... infinitely many solutions, depending on a parameter we usually call "constant"

  • @LuisBorja1981
    @LuisBorja1981 5 ปีที่แล้ว +6

    1:43 I believe I can fly, I believe I can touch the sky

  • @brianlamptey4823
    @brianlamptey4823 5 ปีที่แล้ว

    7:50 I'm guessing that matrix works for any polynomial of degree three or lower since it's composed of the would-be exponents of the terms within such a single variable polynomial.

    • @drpeyam
      @drpeyam  5 ปีที่แล้ว +4

      It works for any polynomial, you would just have a different sized matrix

    • @skeletonrowdie1768
      @skeletonrowdie1768 5 ปีที่แล้ว

      yeah for every polynomial of degree n there is this matrix T which is (n-1) times n. Where that diagonal from element (1,2) contains the positive integers up to n.
      But indeed you extend it with the idea of the would-be components, and by placing every entry of the input vector one place down in the output vector. (bc it's n-1xn)

    • @brianlamptey4823
      @brianlamptey4823 5 ปีที่แล้ว

      @@skeletonrowdie1768 This is be out of context, but are you a Queen fan?

  • @jonasdaverio9369
    @jonasdaverio9369 5 ปีที่แล้ว +1

    Why do you mark your basis vectors with exponents, while they are typically covariant?

    • @drpeyam
      @drpeyam  5 ปีที่แล้ว +1

      At this level it doesn’t matter, and I’m not a geometer, so that’s that, lol

  • @patricksalhany8787
    @patricksalhany8787 5 ปีที่แล้ว +1

    Is P_3 really the notation of the space of the polynomials with degree less than or equal to 3? Weird notation, never saw it before, I know the notation K_3[X], where K is the field of the coefficients of the polynomials.
    In particular for polynomials with coefficients in R and with degree less than or equal to a natural number n, we have R_n[X].

    • @sugarfrosted2005
      @sugarfrosted2005 5 ปีที่แล้ว

      It's literally the only notation I've ever seen. The notation you suggest isn't something I've seen. It doesn't play well with field notation for finite fields.

    • @drpeyam
      @drpeyam  5 ปีที่แล้ว

      Yeah, P3 is legit

    • @crazye7132
      @crazye7132 5 ปีที่แล้ว +2

      In the end it is all just notation

    • @patricksalhany8787
      @patricksalhany8787 5 ปีที่แล้ว +1

      Yes Crazy E, but I find K_n[X] better, because it gives 3 information:
      1. The polynomial is with degree n.
      2. His coefficients are in the field K.
      3. The indeterminate is X.
      To clarify what I'm saying, R_n[X] and C_m[Y] are different in every single way, the fields are different, the degrees are different (assuming n=/=m), and the indeterminates are different.

    • @crazye7132
      @crazye7132 5 ปีที่แล้ว +1

      @@patricksalhany8787 alright, it's the superior one. It is the VIP in the party of notations. But seriously, I am on your side

  • @jakeseals2906
    @jakeseals2906 ปีที่แล้ว

    Thank you!

  • @o_dat
    @o_dat 2 หลายเดือนก่อน

    A very cute problem, he said 💖🎀😊🎀💝

  • @timothy9958
    @timothy9958 5 ปีที่แล้ว +1

    Dr. Peyam after dark

  • @philp4684
    @philp4684 5 ปีที่แล้ว

    That seems like a crazily inefficient way to differentiate in software. Lots of pointless multiplications by zero.
    If a_0, a_1, a_2, a_3, ... are the coefficients of the input, and b_0, b_1, b_2, ... are the coefficients of the derivative, then why not just do:
    b_0 = a_1,
    b_1 = 2 * a_2,
    b_2 = 3 * a_3,
    ...
    b_(n-1) = n * a_n
    ?