So I'm trying to factorize this matrix.
$A= \left( \begin{array}{ccc} 3 & 0 \\ 0 & 3 \\ 4 & 0\\ 0&4 \end{array} \right)$
So I need to remove the 4 at $a_{1,3}$, however I'm a bit confused on how to best do it. I know Householder factorization, but I'm confused on how to do it.
So $Q = I_4 - 2 \times \frac{1}{25} \left( \begin{array}{ccc} -2\\ 0 \\ 4 \\ 0 \end{array} \right) \times (-2,0,4,0)$.
Then, do you just do $QA = R$. I was wondering is there an easier way to work out the QR factorization of this.