LQ decomposition
By Abigail Rogers •
so I'm studying for Dirty Paper Coding on MU-MIMO, the system needs LQ decomposition in it. and I want to ask, where do we get the value of L (as in lower matrix triangular) from this case? can anyone help? thank you so much
$\endgroup$2 Answers
$\begingroup$It is a generalization of QR decomposition. You can read more about LQ decomposition here.
$\endgroup$ 2 $\begingroup$Take an under-determined matrix $A$ and take the transpose, $A^{T}$. Now take the $QR$ decomposition. Now take the transpose of each $Q,R$
$ A = R^{T}Q^{T}$
Like below with some python code.
import numpy as np
A = np.random.rand(10,20)
At = np.transpose(A)
Q,R = np.linalg.qr(At)
Rt = np.transpose(R)
Qt = np.transpose(Q)
error = np.linalg.norm(A - np.dot(Rt,Qt))
print(error)
2.023080674308577e-15
