system of equations with nonlinear constraint

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.

[Torsten]

A11,A12,A13,A22,A23,A33,B are given constants ?

Best wishes

Torsten.

[Mohammadfarid ghasemi]

Yes, x is the 3*1 array of unknowns and the A11,A12,A13,A22,A23,A33,B are the known scalars.

Regards,

Farid

Answer 1

[Torsten]

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.

[Mohammadfarid ghasemi]

You mean I ought to find the eigenvectors of the matrix M? I would be appreciated if you explain in more detail.

Regards, Farid.

[Mohammadfarid ghasemi]

understood, Thank you so much.

Regards,

Farid.

[Torsten]

Take a look at this thread:

https://de.mathworks.com/matlabcentral/answers/328754-rotation-that-maximises-a-vector-length

You search for a vector "that minimizes a vector length".

Best wishes

Torsten.