MATLAB: Solving system of equations

system of matrix

Hi expert,
May I ask your suggestion on how to solve the following matrix system,
where the component of the matrix A is complex numbers with the angle (theta) runs from 0 to 2*pi, and n = 9. The known value z = x + iy = re^ia, is also complex numbers as such, r = sqrt(x^2+y^2) and a = atan (y/x)
Suppose matrix z is as shown below,
z =
         0    1.0148
    0.1736    0.9848
    0.3420    0.9397
    0.5047    0.8742
    0.6748    0.8042
    0.8419    0.7065
    0.9919    0.5727
    1.1049    0.4022
    1.1757    0.2073
    1.1999         0
    1.1757   -0.2073
    1.1049   -0.4022
    0.9919   -0.5727
    0.8419   -0.7065
    0.6748   -0.8042
    0.5047   -0.8742
    0.3420   -0.9397
    0.1736   -0.9848
         0   -1.0148
How do you solve the system of equations above i.e. to find the coefficient of matrix alpha. I tried using a simple matrix manipulation X = inv((tran(A)*A))*tran(A)*z, but I cannot get a reasonable result.
I would expect the solution i.e. components of matrix alpa to be a real numbers.

Best Answer

What do the two columns of z mean? Is the 2nd column supposed to be the imaginary part of z? If so,
Z=complex(z(:,1),z(:,2));
X = A\Z
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