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Homework Help: Vector Basis of R^n

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Let V=(x1,x2,..Xn) Sum X = 0 be a subspace of R^n. Find a basis of V such that Sum X^2=1

    2. Relevant equations



    3. The attempt at a solution
    for Sum X =0

    x1+x2+..+xn =0

    xn= -x1-x2-...

    So <x1, x2, ...,-x1-x2-...>=<x1, 0,0...,-x1> +<0,x2,0,...,-x2)+...

    =x1<1,0,0,...,-1>+x2<0,1,0,...-1>+...
    norm, ||x1||=||x2||=||xn||=... = 2^(1/2)

    Basis {<1/norm x1, 0, 0,..-1/norm x1>, <0,1/normx2,0,...-1/normx2>,...}


    For Sum X^2=0

    x1^2 +x2^2+....+xn^2 =1
    xn^2 = 1- (x1^2 +x2^2+...)

    That all I can do. Please guide me.
     
    Last edited: Sep 16, 2010
  2. jcsd
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