Hi!
I'm new and I need your help, thanks in advance!

I have to perform a LQ factorization of a square matrix in order to get the L matrix; Eigen let do only a QR factorization, so I was wondering if the L matrix and the R matrix are the same, isn't it?

I apologize in advance if my question seems trivial.
Thanks

The L and R matrices are not the same: the L matrix is lower triangular and the R matrix is upper triangular. But the LQ factorization can be easily determined using the LQ factorization. If you want to compute the LQ factorization of a matrix A, then first compute the QR factorization of the transpose of A. Suppose you get A^T = Q2 * R2. Then A = R2^T * Q2^T is the LQ factorization of your original matrix A.

jitseniesen wrote:The L and R matrices are not the same: the L matrix is lower triangular and the R matrix is upper triangular. But the LQ factorization can be easily determined using the LQ factorization. If you want to compute the LQ factorization of a matrix A, then first compute the QR factorization of the transpose of A. Suppose you get A^T = Q2 * R2. Then A = R2^T * Q2^T is the LQ factorization of your original matrix A.

So can I say that L^T = R?

Thanks

Yes, you can see L^T = R as long as you keep in mind that the L is from the LQ decomposition of A and the R is from the QR decomposition of the transpose of A.