MATLAB: Enforce the norm of the addition of two vectors plus scalar

mathematicsMATLAB

Hi,
I have two vectors of the same dimension: and and a scalar β. I'm looking for the value of β such that .
Do you have an idea how to find β ?
Thanks.

Best Answer

  • I assumed that a and b are 3 elements-vector and then solved the equation beta analytically.
    a = [1 2 3];
    b = [2 3 4];
    beta = roots([b(1)^2+b(2)^2+b(3)^2 , 2*(a(1)*b(1)+a(2)*b(2)+a(3)*b(3)),a(1)^2+a(2)^2+a(3)^2-1])
    the result is two solution corresponding to two different value of beta.
    to verify our solution, simply try it;
    norm(a+beta(1)*b)
    or :
    norm(a+beta(2)*b)