Use the Gram-Schmidt process to find an orthonormal basis

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Q. Let S={u_1,u_2,u_3 } with the vectors defined below. S is a basis for R3. Use the Gram-Schmidt process to get an orthonormal basis.
u_1=(1,1,1) u_2=(0,1,1) u_3=(0,0,1)
Every nonzero finite-dimensional inner product space has an orthogonal basis.
#Orthonormal #LinearAlgebra #Projection

Пікірлер: 25

  • @bharathchandrapanasa7997
    @bharathchandrapanasa79977 ай бұрын

    At 2:44 , 1-(2/3) is 1/3. So v3 will be (0, -1/root 2, -1/root 2)

  • @aleksandrailieva5447
    @aleksandrailieva54473 ай бұрын

    Finally somebody that actually explains how to do it in a simple way! Thank you!

  • @goldenrkivee
    @goldenrkivee3 жыл бұрын

    Sir, you just saved my quizzes score, thank you for this simple and easy to understand guide

  • @mahigour7124
    @mahigour71242 жыл бұрын

    This video helps me a lot...Thank You sir

  • @aravindthulasi
    @aravindthulasi4 жыл бұрын

    OMG your sum came to my exam same values

  • @prahladp8849
    @prahladp8849 Жыл бұрын

    great video helped a lot

  • @genesismediavillo9966
    @genesismediavillo99663 жыл бұрын

    Super helpful 🙏

  • @patnamvivek2406
    @patnamvivek24062 жыл бұрын

    Thanks so much really helpful

  • @ma_ncube
    @ma_ncube4 жыл бұрын

    1 - (2/3) isn't negative

  • @StudyForceOnline

    @StudyForceOnline

    4 жыл бұрын

    *My mistake.* Luckily, the rest of the process before and after is correct.

  • @itzelcastaneda6214

    @itzelcastaneda6214

    7 ай бұрын

    ​@@StudyForceOnline just saw this.

  • @amethyst6073
    @amethyst60738 ай бұрын

    Effective and time effective

  • @science__guru2672
    @science__guru2672 Жыл бұрын

    thanks you for this explanation sir😄😄

  • @newtonngigi5528
    @newtonngigi5528 Жыл бұрын

    thanks sir for the help. but I don't understand why you ignored the negative sign.

  • @VodkaTheAntiAlcoholic
    @VodkaTheAntiAlcoholic3 ай бұрын

    Very useful video, but I just wanted to ask why at 1:22 did you mention the ^2 on the denominator if you were going to take norm and square root it anyway? Isn't is pointless to denote ||v||^2 if the square and square root cancel out? I'm definitely missing something here.

  • @baka6777
    @baka67772 жыл бұрын

    Condom ad was coming during my study time🙂🙂🙂🙂

  • @tuyizereangelique8839
    @tuyizereangelique8839 Жыл бұрын

    I have seen where you ignore minus sign!!why that ?or is a mistake 🤷‍♀️

  • @tuyizereangelique8839

    @tuyizereangelique8839

    Жыл бұрын

    There at sub2.i think it should be( -2/3,1/2,1/3).thx

  • @user-jz1vl9tx7f
    @user-jz1vl9tx7f4 ай бұрын

    There was a mistake when subtracting the numbers.1-2/3 must be equal to 1/3 and not -1/3

  • @Jostan748
    @Jostan7484 жыл бұрын

    If you make every number a one or a zero, how is anyone supposed to keep track of which numbers go together? Key steps are being glossed over because 1x1 is obviously 1. Why is every video on this subject as well as my professors so lazy?

  • @itzelcastaneda6214
    @itzelcastaneda62147 ай бұрын

    at 2:43, how is 1-2/3 = -1/3? isn't the same as 3/3-2/3=1/3? Am I missing something?

  • @StudyForceOnline

    @StudyForceOnline

    7 ай бұрын

    1 - (2/3) = 1/3

  • @itzelcastaneda6214

    @itzelcastaneda6214

    7 ай бұрын

    just read the other comments, thank you for the clarification!

  • @yonafat_
    @yonafat_3 жыл бұрын

    sir or anyone please can you explian abuout the last one at sub3 why the result is (0, -1/2, 1/2)??

  • @yonafat_

    @yonafat_

    3 жыл бұрын

    mine is (-1/3, -1/2, 1/2) because they have 3 (-), if two of them match and the last one still minus (-) so, that my result sir