Enforce the norm of the addition of two vectors plus scalar
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Thomas Barbier
il 5 Giu 2019
Modificato: Thomas Barbier
il 5 Giu 2019
Hi,
I have two vectors of the same dimension:
and
and a scalar β. I'm looking for the value of β such that
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/223109/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/223110/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/223118/image.png)
Do you have an idea how to find β ?
Thanks.
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Mohammad Alhashash
il 5 Giu 2019
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)
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