Solving Vector Norm with F Matrix: Advice from Jo

[jollage]

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!
Jo

 

[DonAntonio]

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!
Jo

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

DonAntonio

 

[ajkoer]

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))