I have a matrix consisting of two square matrices A & B

$\displaystyle

C = \begin {pmatrix} A \\ B \end{pmatrix}

$

and I want to perform QR decomposition on C, to obtain it's upper triangular factorization.

My question is, is it possible to perform QR decomposition on matrices A & B seperately, and somehow still obtain the upper triangular factorization of C?