Oxford Linear Algebra: Gram-Schmidt Process

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  • Опубліковано 4 гру 2024

КОМЕНТАРІ • 27

  • @TomRocksMaths
    @TomRocksMaths  Рік тому +3

    Check out ProPrep with a 30-day free trial: www.proprep.uk/info/TOM-Crawford

  • @stevenbercik2099
    @stevenbercik2099 Рік тому +4

    We just covered this in my undergraduate linear algebra class!

  • @franciscodanieldiazgonzale2096
    @franciscodanieldiazgonzale2096 Рік тому +12

    Congratulations for your appointment as Public Engagement Lead and a Departmental Lecturer at the department of continuing education in University of Oxford. We have an Oxford Mathematics Lecturer here people!

  • @ccfzdgfziyj3ybeeyyb860
    @ccfzdgfziyj3ybeeyyb860 Рік тому +6

    Great work professor!

  • @Shaan_Suri
    @Shaan_Suri 6 місяців тому +2

    In the last example, the two vectors only vectors are a basis of polynomials with degree less than or equal to 2. But let's say our vector space was polynomials with degree less than or equal to 3, and we were only given 2 linearly independent vectors, is there a way to construct an orthonormal basis? (ie. extend the orthonormal set with 2 vectors which you found into a set with 3 vectors)

  • @walterblair1646
    @walterblair1646 Рік тому +2

    Hey I reckon you should take a look at the Australian HSC math exams. There's 3 different "hard" ones. Advanced, ext 1 and ext 2. You may just have to brush up on the calculator

  • @eugenek951
    @eugenek951 6 місяців тому

    Thanks for bringing higher math to the "masses" 🙂

  • @narfwhals7843
    @narfwhals7843 10 місяців тому

    Here you show that, given an inner product and a linear independent set we can always create an orthonormal set. Can we go the other way? Can we take a linearly independent set, set it to be orthonormal, and always find an inner product that satisfies this?

  • @bread8586
    @bread8586 Рік тому +1

    At 16:21 is there a difference between the x written like 2 c's and the x written with straight lines?

    • @nacira716
      @nacira716 27 днів тому

      No, they're exactly the same

  • @jorgesalazar2583
    @jorgesalazar2583 Рік тому +1

    What are the reasons for take\int xf(x)g(x)dx as inner product in your last example? Is possible to do G-S process fir a two dimensional space? thanks for your videos

    • @abhinavjain7008
      @abhinavjain7008 9 місяців тому

      I think it's just a way to define the inner product in that question. It doesn't break any of the properties needed for it to be an inner product, so, it's valid.

  • @michelesereni2414
    @michelesereni2414 5 місяців тому

    hello, im sorry if i dont grasp it yet, but isnt the example in the polynomial space not an inner space? shoulnt there be absolute values? if i take g(x) = -x, f(x) = x, then i have the integral of -x^3, which amounts to a negative value? Am I right? or what am I missing? Thank you for your help

  • @pranavkarthik9250
    @pranavkarthik9250 Рік тому +1

    I'm far too dumb to watch this or else i would ... Maybe if i don't have headache or my mother hounding me if i don't get off screen. Love you lots!

    • @rosskious7084
      @rosskious7084 6 місяців тому +1

      Nah…. You could do it. You just have to work up the this point.

  • @AC-tn4it
    @AC-tn4it Рік тому

    Please do modified graham schmidt

  • @alberthagi1310
    @alberthagi1310 Рік тому +1

    Hi tom

  • @ranpancake
    @ranpancake Рік тому +4

    🐐🔥

  • @timothymattnew
    @timothymattnew Рік тому +3

    Isn't Gram-Schmidt process that somehow very intuitively understandable process of turning any basis of an Euclidean space into an ortnonormal basis? I never thought it even had a name because it seems so straightforward.

  • @abelfernandes6862
    @abelfernandes6862 Рік тому

    What's Your Height ?

  • @rileysischo9954
    @rileysischo9954 8 місяців тому

    Yo I have that shirt

  • @somanandi6336
    @somanandi6336 Рік тому +1

    Hi can you please react to jee advanced math paper. It is very tough. It is an exam given by highschool students to get into respectable colleges IIT

  • @mathswala2664
    @mathswala2664 Рік тому

    Hlo, give answer of this question.
    Number of tangents of curve y=e^|x| at (0, 1),
    Options are
    a) 2, b) 4, c) 1,d) 0

  • @Gj-8422
    @Gj-8422 Рік тому

    Do you have any maths videos for normal people, who are not oxbridge educated?

    • @DarkKittens123
      @DarkKittens123 7 місяців тому +3

      Dude this is for normal people, it’s just linear algebra