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Doubts on vector norm!

  1. Apr 12, 2012 #1
    Hi guys

    Assume F to be a square matrix, say 3 by 3. Now I want to find a vector q (3 by 1) to meet the requirement that norm(F*q)=1. How can I find it? What is the solution in general?

    THanks in advance!!
  2. jcsd
  3. Apr 12, 2012 #2

    Let v be any vector s.t. [itex]Fv\neq 0[/itex] and let [itex]q:=\frac{v}{||Fv||}[/itex]

  4. Apr 12, 2012 #3
    a b c * [k l m]' = [ak+bl+cm, ek+fl+gm, hk+il+jm]'
    e f g
    h i j

    So we need (k, l , m) such that:
    (ak+bl+cm)^2+ (ek+fl+gm)^2 + (hk+il+jm)^2 = 1

    Answer, first chose l = m = 0, so we need:
    a^2 + e^2 + h^2 = 1/k^2

    or k = sqrt (1/(a^2 + e^2 + h^2))
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