15 views (last 30 days)

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.

Matt J
on 1 Jan 2018

Edited: Matt J
on 1 Jan 2018

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

Matt J
on 17 Feb 2018

If the first value is 1, then this just leads to a mild modification of my initial proposal,

zc=complex(z(:,1),z(:,2));

alpha=A(:,2:end)\(zc-A(:,1))

This solves for the unknown alpha (alpha2,...,alphaN).

Jan
on 25 Apr 2019

Opportunities for recent engineering grads.

Apply TodayFind the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
## 0 Comments

Sign in to comment.