If you have two complex numbers $a,b$ how can you find the QR factorization of
$ M = \begin{bmatrix} aI_n\\ bI_n \end{bmatrix} $,
I can't seem to be able to do it. I tried an earlier trick, but I now know it's not necessary true for complex numbers. Is there anyway to do this?
I think if I use a Givens algorithm I should be able to reduce it to a QR factorization.