Solving linear equation of complex matrices-CodePudding

I have a linear equation of a form ax=b where b is a complex matrix, and a is a real matrix. I'm expecting solution x to be a complex vector. When trying the numpy.linalg.solve(a,b) function, I'm getting this warning:

ComplexWarning: Casting complex values to real discards the imaginary part

How do I solve this equation to preserve the complex numbers?

CodePudding user response：

Split b into its real and imaginary components and solve the real/imaginary parts separately
Ax = b = A(xr xi) = br bi
A @ xr = br, A @ xi = bi

br = np.real(b)
bi = np.imag(b)
A_inv = np.linalg.inv(A)
xr = A_inv @ br
xi = A_inv @ bi
x = xr   1.j*xi

EDIT The way you want to do it:

x = np.linalg.solve(A, np.real(b))   1.j*np.linalg.solve(A, np.imag(b))