I'm supposed to do a variety of matlab experiments for different factorizations and two of those are QR and LQ factorizations, which for matrix $A$ ${m \times n}$ yield $$A=Q[R_1\;R_2]$$ where $R_1$ is upper triangular of order m, $R_2$ is $m\times(n-m)$ and Q is orthogonal of order m, and $$A=[L\;0]Q,$$ where $L$ is lower triangular of order m, Q is orthogonal of order n. Supposedly LQ is calculated by applying QR on $A^T$ and transposing it back.
I found very few resources regarding LQ factorization, so my question is, why would we ever really want to use LQ instead of QR? I'm not sure about its purpose.