I have a problem. Given

\ Ax = \lambda x

and the QR factorization

\ x = Qr = Q \begin{bmatrix} r_1 \\ 0 \end{bmatrix}

Using these two equations I want to SHOW that


 Q^H AQ = \begin{bmatrix} \lambda & T_{12} \\ 0 & T_{22} \end{bmatrix}

Now Q is unitary i.e
\ Q^H Q = QQ^H = I

Can you show me how to do this?