Let $A \in M_n(\mathbb C)$ and $\lambda_1,\lambda_2,...\lambda_n$ be eigenvalues. Let $x$ be a eigenvector of $\lambda_1$ such that $x^*x=1$ and $U_1$ be a unitary matrix with the columns $[x_1,u_2,...,u_n]$ show that $U^*AU$ has the form $$\pmatrix{\lambda_1 & w \\ 0 & A_1 }$$
where $A_1$ carry matrix of order $n-1$ and $w$ line vector $\mathbb C^{n-1}$.\
I'm absolute beginner to block matrix but i now that $Ax_1=\lambda x_1$ and $U^*U= I$. Can you help me