MATLAB: System of equations with nonlinear constraint

nonlinear constraintsoptimizationsystem of equations

Hi, I have a system of three linear equations and three unknowns as below:
x(1).*(A11-B)+x(2).*A12+x(3).*A13=0
x(1).*A12 +x(2).*(A22-B)+x(3).*A23=0
x(1).*A13 +x(3).*(A33-B)+x(2).*A23=0
applying the fsolve yields the obvious answer of [0 0 0], Therefore, I have to define the following nonlinear and linear constraints:
x(1)^2+x(2)^2+x(3)^2=1.0 & -1<=x(1),x(2),x(3)<=1
I'm familiar with fmincon but it is applicable for scalar functions when one wants to find min f(x). I wonder how can I solve the aforementioned problem? Thank you so much for your time and attention.

Best Answer

Then x is a normalized eigenvector to the minimum eigenvalue of the matrix
M=A*transpose(A)
where
A=[A11-B A12 A13;A12 A22-B A23;A13 A23 A33-B]
help eig
Best wishes
Torsten.
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