Orthogonal transformation of matrix

[vabamyyr]

I have a question on matrix norms and orthogonal transformations. The 2-norm in invariant under orthogonal transformation, for if Q^T*Q=I. But i have trouble showing that for orthogonal Q and Q^H with appropriate dimensions

|| Q^H*A*Q ||2 =|| A ||2

 

[doodle]

The 2-norm of A returns the square-root of the maximum absolute eigenvalues of A^HA. So check, does (Q^HA*Q)^HQ^HA*Q preserve the absolute eigenvalues of A^HA?